Merge branch 'master' into edge_collapse_integration_vincent

19 files changed, 1116 insertions, 188 deletions

diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
index c19ebb79..f56e12d0 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
@@ -14,6 +14,9 @@
 
 #include <boost/version.hpp>
 #include <boost/variant.hpp>
+#include <boost/range/size.hpp>
+#include <boost/range/combine.hpp>
+#include <boost/range/adaptor/transformed.hpp>
 
 #include <gudhi/Debug_utils.h>
 #include <gudhi/Alpha_complex_options.h>
@@ -277,8 +280,8 @@ Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Bare_
   Alpha_complex_3d(const InputPointRange& points) {
     static_assert(!Periodic, "This constructor is not available for periodic versions of Alpha_complex_3d");
 
-    alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(
-        new Alpha_shape_3(std::begin(points), std::end(points), 0, Alpha_shape_3::GENERAL));
+    alpha_shape_3_ptr_ = std::make_unique<Alpha_shape_3>(
+        std::begin(points), std::end(points), 0, Alpha_shape_3::GENERAL);
   }
 
   /** \brief Alpha_complex constructor from a list of points and associated weights.
@@ -299,20 +302,15 @@ Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Bare_
   Alpha_complex_3d(const InputPointRange& points, WeightRange weights) {
     static_assert(Weighted, "This constructor is not available for non-weighted versions of Alpha_complex_3d");
     static_assert(!Periodic, "This constructor is not available for periodic versions of Alpha_complex_3d");
-    GUDHI_CHECK((weights.size() == points.size()),
+    // FIXME: this test is only valid if we have a forward range
+    GUDHI_CHECK(boost::size(weights) == boost::size(points),
                 std::invalid_argument("Points number in range different from weights range number"));
 
-    std::vector<Weighted_point_3> weighted_points_3;
+    auto weighted_points_3 = boost::range::combine(points, weights)
+      | boost::adaptors::transformed([](auto const&t){return Weighted_point_3(boost::get<0>(t), boost::get<1>(t));});
 
-    std::size_t index = 0;
-    weighted_points_3.reserve(points.size());
-    while ((index < weights.size()) && (index < points.size())) {
-      weighted_points_3.push_back(Weighted_point_3(points[index], weights[index]));
-      index++;
-    }
-
-    alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(
-        new Alpha_shape_3(std::begin(weighted_points_3), std::end(weighted_points_3), 0, Alpha_shape_3::GENERAL));
+    alpha_shape_3_ptr_ = std::make_unique<Alpha_shape_3>(
+        std::begin(weighted_points_3), std::end(weighted_points_3), 0, Alpha_shape_3::GENERAL);
   }
 
   /** \brief Alpha_complex constructor from a list of points and an iso-cuboid coordinates.
@@ -356,7 +354,7 @@ Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Bare_
 
     // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode. This is the default mode
     // Maybe need to set it to GENERAL mode
-    alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(new Alpha_shape_3(pdt, 0, Alpha_shape_3::GENERAL));
+    alpha_shape_3_ptr_ = std::make_unique<Alpha_shape_3>(pdt, 0, Alpha_shape_3::GENERAL);
   }
 
   /** \brief Alpha_complex constructor from a list of points, associated weights and an iso-cuboid coordinates.
@@ -388,31 +386,27 @@ Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Bare_
                    FT z_min, FT x_max, FT y_max, FT z_max) {
     static_assert(Weighted, "This constructor is not available for non-weighted versions of Alpha_complex_3d");
     static_assert(Periodic, "This constructor is not available for non-periodic versions of Alpha_complex_3d");
-    GUDHI_CHECK((weights.size() == points.size()),
+    // FIXME: this test is only valid if we have a forward range
+    GUDHI_CHECK(boost::size(weights) == boost::size(points),
                 std::invalid_argument("Points number in range different from weights range number"));
     // Checking if the cuboid is the same in x,y and z direction. If not, CGAL will not process it.
     GUDHI_CHECK(
         (x_max - x_min == y_max - y_min) && (x_max - x_min == z_max - z_min) && (z_max - z_min == y_max - y_min),
         std::invalid_argument("The size of the cuboid in every directions is not the same."));
 
-    std::vector<Weighted_point_3> weighted_points_3;
-
-    std::size_t index = 0;
-    weighted_points_3.reserve(points.size());
-
 #ifdef GUDHI_DEBUG
     // Defined in GUDHI_DEBUG to avoid unused variable warning for GUDHI_CHECK
     FT maximal_possible_weight = 0.015625 * (x_max - x_min) * (x_max - x_min);
 #endif
 
-    while ((index < weights.size()) && (index < points.size())) {
-      GUDHI_CHECK((weights[index] < maximal_possible_weight) && (weights[index] >= 0),
-                  std::invalid_argument("Invalid weight at index " + std::to_string(index + 1) +
-                                        ". Must be positive and less than maximal possible weight = 1/64*cuboid length "
-                                        "squared, which is not an acceptable input."));
-      weighted_points_3.push_back(Weighted_point_3(points[index], weights[index]));
-      index++;
-    }
+    auto weighted_points_3 = boost::range::combine(points, weights)
+      | boost::adaptors::transformed([=](auto const&t){
+          auto w = boost::get<1>(t);
+          GUDHI_CHECK((w < maximal_possible_weight) && (w >= 0),
+              std::invalid_argument("Invalid weight " + std::to_string(w) +
+                ". Must be non-negative and less than maximal possible weight = 1/64*cuboid length squared."));
+          return Weighted_point_3(boost::get<0>(t), w);
+          });
 
     // Define the periodic cube
     Dt pdt(typename Kernel::Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max));
@@ -426,7 +420,7 @@ Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Bare_
 
     // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode. This is the default mode
     // Maybe need to set it to GENERAL mode
-    alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(new Alpha_shape_3(pdt, 0, Alpha_shape_3::GENERAL));
+    alpha_shape_3_ptr_ = std::make_unique<Alpha_shape_3>(pdt, 0, Alpha_shape_3::GENERAL);
   }
 
   /** \brief Inserts all Delaunay triangulation into the simplicial complex.
@@ -471,6 +465,10 @@ Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Bare_
 #ifdef DEBUG_TRACES
     std::clog << "filtration_with_alpha_values returns : " << objects.size() << " objects" << std::endl;
 #endif  // DEBUG_TRACES
+    if (objects.size() == 0) {
+      std::cerr << "Alpha_complex_3d create_complex - no triangulation as points are on a 2d plane\n";
+      return false;  // ----- >>
+    }
 
     using Alpha_value_iterator = typename std::vector<FT>::const_iterator;
     Alpha_value_iterator alpha_value_iterator = alpha_values.begin();
diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt
index 81be1b76..4f26481e 100644
--- a/src/python/CMakeLists.txt
+++ b/src/python/CMakeLists.txt
@@ -14,6 +14,15 @@ function( add_GUDHI_PYTHON_lib THE_LIB )
   endif(EXISTS ${THE_LIB})
 endfunction( add_GUDHI_PYTHON_lib )
 
+function( add_GUDHI_PYTHON_lib_dir THE_LIB_DIR )
+  # deals when it is not set - error on windows
+  if(EXISTS ${THE_LIB_DIR})
+    set(GUDHI_PYTHON_LIBRARY_DIRS "${GUDHI_PYTHON_LIBRARY_DIRS}'${THE_LIB_DIR}', " PARENT_SCOPE)
+  else()
+    message("add_GUDHI_PYTHON_lib_dir - '${THE_LIB_DIR}' does not exist")
+  endif()
+endfunction( add_GUDHI_PYTHON_lib_dir )
+
 # THE_TEST is the python test file name (without .py extension) containing tests functions
 function( add_gudhi_py_test THE_TEST )
   if(PYTEST_FOUND)
@@ -36,6 +45,7 @@ if(PYTHONINTERP_FOUND)
     add_gudhi_debug_info("Pybind11 version ${PYBIND11_VERSION}")
     set(GUDHI_PYTHON_MODULES "${GUDHI_PYTHON_MODULES}'bottleneck', ")
     set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'hera', ")
+    set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'clustering', ")
   endif()
   if(CYTHON_FOUND)
     set(GUDHI_PYTHON_MODULES "${GUDHI_PYTHON_MODULES}'off_reader', ")
@@ -130,6 +140,7 @@ if(PYTHONINTERP_FOUND)
     set(GUDHI_CYTHON_MODULES "${GUDHI_CYTHON_MODULES}'reader_utils', ")
     set(GUDHI_CYTHON_MODULES "${GUDHI_CYTHON_MODULES}'witness_complex', ")
     set(GUDHI_CYTHON_MODULES "${GUDHI_CYTHON_MODULES}'strong_witness_complex', ")
+    set(GUDHI_PYBIND11_MODULES "${GUDHI_PYBIND11_MODULES}'clustering/_tomato', ")
     set(GUDHI_PYBIND11_MODULES "${GUDHI_PYBIND11_MODULES}'hera/wasserstein', ")
     set(GUDHI_PYBIND11_MODULES "${GUDHI_PYBIND11_MODULES}'hera/bottleneck', ")
     if (NOT CGAL_VERSION VERSION_LESS 4.11.0)
@@ -152,7 +163,7 @@ if(PYTHONINTERP_FOUND)
       else(CGAL_HEADER_ONLY)
         add_gudhi_debug_info("CGAL version ${CGAL_VERSION}")
         add_GUDHI_PYTHON_lib("${CGAL_LIBRARY}")
-        set(GUDHI_PYTHON_LIBRARY_DIRS "${GUDHI_PYTHON_LIBRARY_DIRS}'${CGAL_LIBRARIES_DIR}', ")
+        add_GUDHI_PYTHON_lib_dir("${CGAL_LIBRARIES_DIR}")
         message("** Add CGAL ${CGAL_LIBRARIES_DIR}")
         # If CGAL is not header only, CGAL library may link with boost system,
         if(CMAKE_BUILD_TYPE MATCHES Debug)
@@ -160,7 +171,7 @@ if(PYTHONINTERP_FOUND)
         else()
           add_GUDHI_PYTHON_lib("${Boost_SYSTEM_LIBRARY_RELEASE}")
         endif()
-        set(GUDHI_PYTHON_LIBRARY_DIRS "${GUDHI_PYTHON_LIBRARY_DIRS}'${Boost_LIBRARY_DIRS}', ")
+        add_GUDHI_PYTHON_lib_dir("${Boost_LIBRARY_DIRS}")
         message("** Add Boost ${Boost_LIBRARY_DIRS}")
       endif(CGAL_HEADER_ONLY)
       # GMP and GMPXX are not required, but if present, CGAL will link with them.
@@ -168,13 +179,17 @@ if(PYTHONINTERP_FOUND)
         add_gudhi_debug_info("GMP_LIBRARIES = ${GMP_LIBRARIES}")
         set(GUDHI_PYTHON_EXTRA_COMPILE_ARGS "${GUDHI_PYTHON_EXTRA_COMPILE_ARGS}'-DCGAL_USE_GMP', ")
         add_GUDHI_PYTHON_lib("${GMP_LIBRARIES}")
-        set(GUDHI_PYTHON_LIBRARY_DIRS "${GUDHI_PYTHON_LIBRARY_DIRS}'${GMP_LIBRARIES_DIR}', ")
+        if(NOT GMP_LIBRARIES_DIR)
+          get_filename_component(GMP_LIBRARIES_DIR ${GMP_LIBRARIES} PATH)
+          message("GMP_LIBRARIES_DIR from GMP_LIBRARIES set to ${GMP_LIBRARIES_DIR}")
+        endif(NOT GMP_LIBRARIES_DIR)
+        add_GUDHI_PYTHON_lib_dir("${GMP_LIBRARIES_DIR}")
         message("** Add gmp ${GMP_LIBRARIES_DIR}")
         if(GMPXX_FOUND)
           add_gudhi_debug_info("GMPXX_LIBRARIES = ${GMPXX_LIBRARIES}")
           set(GUDHI_PYTHON_EXTRA_COMPILE_ARGS "${GUDHI_PYTHON_EXTRA_COMPILE_ARGS}'-DCGAL_USE_GMPXX', ")
           add_GUDHI_PYTHON_lib("${GMPXX_LIBRARIES}")
-          set(GUDHI_PYTHON_LIBRARY_DIRS "${GUDHI_PYTHON_LIBRARY_DIRS}'${GMPXX_LIBRARIES_DIR}', ")
+          add_GUDHI_PYTHON_lib_dir("${GMPXX_LIBRARIES_DIR}")
           message("** Add gmpxx ${GMPXX_LIBRARIES_DIR}")
         endif(GMPXX_FOUND)
       endif(GMP_FOUND)
@@ -185,9 +200,10 @@ if(PYTHONINTERP_FOUND)
         # In case CGAL is not header only, all MPFR variables are set except MPFR_LIBRARIES_DIR - Just set it
         if(NOT MPFR_LIBRARIES_DIR)
           get_filename_component(MPFR_LIBRARIES_DIR ${MPFR_LIBRARIES} PATH)
+          message("MPFR_LIBRARIES_DIR from MPFR_LIBRARIES set to ${MPFR_LIBRARIES_DIR}")
         endif(NOT MPFR_LIBRARIES_DIR)
-        set(GUDHI_PYTHON_LIBRARY_DIRS "${GUDHI_PYTHON_LIBRARY_DIRS}'${MPFR_LIBRARIES_DIR}', ")
-        message("** Add mpfr ${MPFR_LIBRARIES}")
+        add_GUDHI_PYTHON_lib_dir("${MPFR_LIBRARIES_DIR}")
+        message("** Add mpfr ${MPFR_LIBRARIES_DIR}")
       endif(MPFR_FOUND)
     endif(CGAL_FOUND)
 
@@ -214,7 +230,7 @@ if(PYTHONINTERP_FOUND)
         add_GUDHI_PYTHON_lib("${TBB_RELEASE_LIBRARY}")
         add_GUDHI_PYTHON_lib("${TBB_MALLOC_RELEASE_LIBRARY}")
       endif()
-      set(GUDHI_PYTHON_LIBRARY_DIRS "${GUDHI_PYTHON_LIBRARY_DIRS}'${TBB_LIBRARY_DIRS}', ")
+      add_GUDHI_PYTHON_lib_dir("${TBB_LIBRARY_DIRS}")
       message("** Add tbb ${TBB_LIBRARY_DIRS}")
       set(GUDHI_PYTHON_INCLUDE_DIRS "${GUDHI_PYTHON_INCLUDE_DIRS}'${TBB_INCLUDE_DIRS}', ")
     endif()
@@ -235,6 +251,7 @@ if(PYTHONINTERP_FOUND)
     file(COPY "gudhi/representations" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi/")
     file(COPY "gudhi/wasserstein" 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")
     file(COPY "gudhi/dtm_rips_complex.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
     file(COPY "gudhi/hera/__init__.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi/hera")
@@ -499,6 +516,11 @@ if(PYTHONINTERP_FOUND)
       add_gudhi_py_test(test_dtm)
     endif()
 
+    # Tomato
+    if(SCIPY_FOUND AND SKLEARN_FOUND AND PYBIND11_FOUND)
+      add_gudhi_py_test(test_tomato)
+    endif()
+
     # Weighted Rips
     if(SCIPY_FOUND)
       add_gudhi_py_test(test_weighted_rips_complex)
diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst
index 097470c1..fffcb3db 100644
--- a/src/python/doc/alpha_complex_user.rst
+++ b/src/python/doc/alpha_complex_user.rst
@@ -34,8 +34,8 @@ Remarks
   the computation of filtration values can exceptionally be arbitrarily bad. In all cases, we still guarantee that the
   output is a valid filtration (faces have a filtration value no larger than their cofaces).
 * For performances reasons, it is advised to use Alpha_complex with `CGAL <installation.html#cgal>`_ :math:`\geq` 5.0.0.
-
-For performances reasons, it is advised to use CGAL :math:`\geq` 5.0.0.
+* The vertices in the output simplex tree are not guaranteed to match the order of the input points. One can use
+  :func:`~gudhi.AlphaComplex.get_point` to get the initial point back.
 
 Example from points
 -------------------
@@ -178,49 +178,22 @@ In the following example, a threshold of :math:`\alpha^2 = 32.0` is used.
 Example from OFF file
 ^^^^^^^^^^^^^^^^^^^^^
 
-This example builds the Delaunay triangulation from the points given by an OFF file, and initializes the alpha complex
-with it.
-
+This example builds the alpha complex from 300 random points on a 2-torus.
 
-Then, it is asked to display information about the alpha complex:
+Then, it computes the persistence diagram and displays it:
 
-.. testcode::
+.. plot::
+   :include-source:
 
+    import matplotlib.pyplot as plt
     import gudhi
     alpha_complex = gudhi.AlphaComplex(off_file=gudhi.__root_source_dir__ + \
-        '/data/points/alphacomplexdoc.off')
-    simplex_tree = alpha_complex.create_simplex_tree(max_alpha_square=32.0)
+        '/data/points/tore3D_300.off')
+    simplex_tree = alpha_complex.create_simplex_tree()
     result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
         repr(simplex_tree.num_simplices()) + ' simplices - ' + \
         repr(simplex_tree.num_vertices()) + ' vertices.'
     print(result_str)
-    fmt = '%s -> %.2f'
-    for filtered_value in simplex_tree.get_filtration():
-        print(fmt % tuple(filtered_value))
-
-the program output is:
-
-.. testoutput::
-
-   Alpha complex is of dimension 2 - 20 simplices - 7 vertices.
-   [0] -> 0.00
-   [1] -> 0.00
-   [2] -> 0.00
-   [3] -> 0.00
-   [4] -> 0.00
-   [5] -> 0.00
-   [6] -> 0.00
-   [2, 3] -> 6.25
-   [4, 5] -> 7.25
-   [0, 2] -> 8.50
-   [0, 1] -> 9.25
-   [1, 3] -> 10.00
-   [1, 2] -> 11.25
-   [1, 2, 3] -> 12.50
-   [0, 1, 2] -> 13.00
-   [5, 6] -> 13.25
-   [2, 4] -> 20.00
-   [4, 6] -> 22.74
-   [4, 5, 6] -> 22.74
-   [3, 6] -> 30.25
-
+    diag = simplex_tree.persistence()
+    gudhi.plot_persistence_diagram(diag)
+    plt.show()
diff --git a/src/python/doc/clustering.inc b/src/python/doc/clustering.inc
new file mode 100644
index 00000000..2d07ae88
--- /dev/null
+++ b/src/python/doc/clustering.inc
@@ -0,0 +1,12 @@
+.. table::
+   :widths: 30 40 30
+
+   +--------------------------+-------------------------------------------------------+---------------------------------+
+   | .. figure::              | Clustering tools.                                     | :Author: Marc Glisse            |
+   |     img/spiral-color.png |                                                       |                                 |
+   |                          |                                                       | :Since: GUDHI 3.3.0             |
+   |                          |                                                       |                                 |
+   |                          |                                                       | :License: MIT                   |
+   +--------------------------+-------------------------------------------------------+---------------------------------+
+   | * :doc:`clustering`                                                                                                |
+   +--------------------------+-----------------------------------------------------------------------------------------+
diff --git a/src/python/doc/clustering.rst b/src/python/doc/clustering.rst
new file mode 100644
index 00000000..c5a57d3c
--- /dev/null
+++ b/src/python/doc/clustering.rst
@@ -0,0 +1,73 @@
+:orphan:
+
+.. To get rid of WARNING: document isn't included in any toctree
+
+=================
+Clustering manual
+=================
+
+We provide an implementation of ToMATo :cite:`tomato`, a persistence-based clustering algorithm. In short, this algorithm uses a density estimator and a neighborhood graph, starts with a mode-seeking phase (naive hill-climbing) to build initial clusters, and finishes by merging clusters based on their prominence.
+
+The merging phase depends on a parameter, which is the minimum prominence a cluster needs to avoid getting merged into another, bigger cluster. This parameter determines the number of clusters, and for convenience we allow you to choose instead the number of clusters. Decreasing the prominence threshold defines a hierarchy of clusters: if 2 points are in separate clusters when we have k clusters, they are still in different clusters for k+1 clusters.
+
+As a by-product, we produce the persistence diagram of the merge tree of the initial clusters. This is a convenient graphical tool to help decide how many clusters we want.
+
+.. plot::
+   :context:
+   :include-source:
+
+   import gudhi
+   f = open(gudhi.__root_source_dir__ + '/data/points/spiral_2d.csv', 'r')
+   import numpy as np
+   data = np.loadtxt(f)
+   import matplotlib.pyplot as plt
+   plt.scatter(data[:,0],data[:,1],marker='.',s=1)
+   plt.show()
+
+.. plot::
+   :context: close-figs
+   :include-source:
+
+   from gudhi.clustering.tomato import Tomato
+   t = Tomato()
+   t.fit(data)
+   t.plot_diagram()
+
+As one can see in `t.n_clusters_`, the algorithm found 6316 initial clusters. The diagram shows their prominence as their distance to the diagonal. There is always one point infinitely far: there is at least one cluster. Among the others, one point seems significantly farther from the diagonal than the others, which indicates that splitting the points into 2 clusters may be a sensible idea.
+
+.. plot::
+   :context: close-figs
+   :include-source:
+
+   t.n_clusters_=2
+   plt.scatter(data[:,0],data[:,1],marker='.',s=1,c=t.labels_)
+   plt.show()
+
+Of course this is just the result for one set of parameters. We can ask for a different density estimator and a different neighborhood graph computed with different parameters.
+
+.. plot::
+   :context: close-figs
+   :include-source:
+
+   t = Tomato(density_type='DTM', k=100)
+   t.fit(data)
+   t.plot_diagram()
+
+Makes the number of clusters clearer, and changes a bit the shape of the clusters.
+
+A quick look at the corresponding density estimate
+
+.. plot::
+   :context: close-figs
+   :include-source:
+
+   plt.scatter(data[:,0],data[:,1],marker='.',s=1,c=t.weights_)
+   plt.show()
+
+The code provides a few density estimators and graph constructions for convenience when first experimenting, but it is actually expected that advanced users provide their own graph and density estimates instead of point coordinates.
+
+Since the algorithm essentially computes basins of attraction, it is also encouraged to use it on functions that do not represent densities at all.
+
+.. autoclass:: gudhi.clustering.tomato.Tomato
+   :members:
+   :special-members: __init__
diff --git a/src/python/doc/img/spiral-color.png b/src/python/doc/img/spiral-color.png
new file mode 100644
index 00000000..21b62dfc
--- /dev/null
+++ b/src/python/doc/img/spiral-color.png
diff --git a/src/python/doc/index.rst b/src/python/doc/index.rst
index 05bc18b4..040e57a4 100644
--- a/src/python/doc/index.rst
+++ b/src/python/doc/index.rst
@@ -86,3 +86,8 @@ Point cloud utilities
 *********************
 
 .. include:: point_cloud_sum.inc
+
+Clustering
+**********
+
+.. include:: clustering.inc
diff --git a/src/python/gudhi/alpha_complex.pyx b/src/python/gudhi/alpha_complex.pyx
index a356384d..ea128743 100644
--- a/src/python/gudhi/alpha_complex.pyx
+++ b/src/python/gudhi/alpha_complex.pyx
@@ -20,6 +20,7 @@ import os
 
 from gudhi.simplex_tree cimport *
 from gudhi.simplex_tree import SimplexTree
+from gudhi import read_points_from_off_file
 
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
@@ -27,11 +28,9 @@ __license__ = "GPL v3"
 
 cdef extern from "Alpha_complex_interface.h" namespace "Gudhi":
     cdef cppclass Alpha_complex_interface "Gudhi::alpha_complex::Alpha_complex_interface":
-        Alpha_complex_interface(vector[vector[double]] points, bool fast_version) nogil except +
-        # bool from_file is a workaround for cython to find the correct signature
-        Alpha_complex_interface(string off_file, bool fast_version, bool from_file) nogil except +
+        Alpha_complex_interface(vector[vector[double]] points, bool fast_version, bool exact_version) nogil except +
         vector[double] get_point(int vertex) nogil except +
-        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square, bool exact_version, bool default_filtration_value) nogil except +
+        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square, bool default_filtration_value) nogil except +
 
 # AlphaComplex python interface
 cdef class AlphaComplex:
@@ -54,7 +53,6 @@ cdef class AlphaComplex:
     """
 
     cdef Alpha_complex_interface * this_ptr
-    cdef bool exact
 
     # Fake constructor that does nothing but documenting the constructor
     def __init__(self, points=None, off_file='', precision='safe'):
@@ -76,21 +74,20 @@ cdef class AlphaComplex:
     def __cinit__(self, points = None, off_file = '', precision = 'safe'):
         assert precision in ['fast', 'safe', 'exact'], "Alpha complex precision can only be 'fast', 'safe' or 'exact'"
         cdef bool fast = precision == 'fast'
-        self.exact = precision == 'exact'
+        cdef bool exact = precision == 'exact'
 
         cdef vector[vector[double]] pts
         if off_file:
             if os.path.isfile(off_file):
-                self.this_ptr = new Alpha_complex_interface(off_file.encode('utf-8'), fast, True)
+                points = read_points_from_off_file(off_file = off_file)
             else:
                 print("file " + off_file + " not found.")
-        else:
-            if points is None:
-                # Empty Alpha construction
-                points=[]
-            pts = points
-            with nogil:
-                self.this_ptr = new Alpha_complex_interface(pts, fast)
+        if points is None:
+            # Empty Alpha construction
+            points=[]
+        pts = points
+        with nogil:
+            self.this_ptr = new Alpha_complex_interface(pts, fast, exact)
 
     def __dealloc__(self):
         if self.this_ptr != NULL:
@@ -102,7 +99,7 @@ cdef class AlphaComplex:
         return self.this_ptr != NULL
 
     def get_point(self, vertex):
-        """This function returns the point corresponding to a given vertex.
+        """This function returns the point corresponding to a given vertex from the :class:`~gudhi.SimplexTree`.
 
         :param vertex: The vertex.
         :type vertex: int
@@ -128,5 +125,5 @@ cdef class AlphaComplex:
         cdef bool compute_filtration = default_filtration_value == True
         with nogil:
             self.this_ptr.create_simplex_tree(<Simplex_tree_interface_full_featured*>stree_int_ptr,
-                                              mas, self.exact, compute_filtration)
+                                              mas, compute_filtration)
         return stree
diff --git a/src/python/gudhi/clustering/__init__.py b/src/python/gudhi/clustering/__init__.py
new file mode 100644
index 00000000..e69de29b
--- /dev/null
+++ b/src/python/gudhi/clustering/__init__.py
diff --git a/src/python/gudhi/clustering/_tomato.cc b/src/python/gudhi/clustering/_tomato.cc
new file mode 100644
index 00000000..a76a2c3a
--- /dev/null
+++ b/src/python/gudhi/clustering/_tomato.cc
@@ -0,0 +1,277 @@
+/*    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):       Marc Glisse
+ *
+ *    Copyright (C) 2020 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#include <boost/container/flat_map.hpp>
+#include <boost/pending/disjoint_sets.hpp>
+#include <boost/property_map/property_map.hpp>
+#include <boost/property_map/transform_value_property_map.hpp>
+#include <boost/property_map/vector_property_map.hpp>
+#include <boost/property_map/function_property_map.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/irange.hpp>
+#include <boost/range/adaptor/transformed.hpp>
+#include <vector>
+#include <unordered_map>
+#include <pybind11/pybind11.h>
+#include <pybind11/numpy.h>
+#include <iostream>
+
+namespace py = pybind11;
+
+template <class T, class = std::enable_if_t<std::is_integral<T>::value>>
+int getint(int i) {
+  return i;
+}
+// Gcc-8 has a bug that breaks this version, fixed in gcc-9
+// template<class T, class=decltype(std::declval<T>().template cast<int>())>
+// int getint(T i){return i.template cast<int>();}
+template <class T>
+auto getint(T i) -> decltype(i.template cast<int>()) {
+  return i.template cast<int>();
+}
+
+// Raw clusters are clusters obtained through single-linkage, no merging.
+
+typedef int Point_index;
+typedef int Cluster_index;
+struct Merge {
+  Cluster_index first, second;
+  double persist;
+};
+
+template <class Neighbors, class Density, class Order, class ROrder>
+auto tomato(Point_index num_points, Neighbors const& neighbors, Density const& density, Order const& order,
+            ROrder const& rorder) {
+  // point index --> index of raw cluster it belongs to
+  std::vector<Cluster_index> raw_cluster;
+  raw_cluster.reserve(num_points);
+  // cluster index --> index of top point in the cluster
+  Cluster_index n_raw_clusters = 0;  // current number of raw clusters seen
+  //
+  std::vector<Merge> merges;
+  struct Data {
+    Cluster_index parent;
+    int rank;
+    Point_index max;
+  };  // information on a cluster
+  std::vector<Data> ds_base;
+  // boost::vector_property_map does resize(size+1) for every new element, don't use it
+  auto ds_data =
+      boost::make_function_property_map<std::size_t>([&ds_base](std::size_t n) -> Data& { return ds_base[n]; });
+  auto ds_parent =
+      boost::make_transform_value_property_map([](auto& p) -> Cluster_index& { return p.parent; }, ds_data);
+  auto ds_rank = boost::make_transform_value_property_map([](auto& p) -> int& { return p.rank; }, ds_data);
+  boost::disjoint_sets<decltype(ds_rank), decltype(ds_parent)> ds(
+      ds_rank, ds_parent);                         // on the clusters, not directly the points
+  std::vector<std::array<double, 2>> persistence;  // diagram (finite points)
+  boost::container::flat_map<Cluster_index, Cluster_index>
+      adj_clusters;  // first: the merged cluster, second: the raw cluster
+  // we only care about the raw cluster, we could use a vector to store the second, store first into a set, and only
+  // insert in the vector if merged is absent from the set
+
+  for (Point_index i = 0; i < num_points; ++i) {
+    // auto&& ngb = neighbors[order[i]];
+    // TODO: have a specialization where we don't need python types and py::cast
+    // TODO: move py::cast and getint into Neighbors
+    py::object ngb = neighbors[py::cast(order[i])];  // auto&& also seems to work
+    adj_clusters.clear();
+    Point_index j = i;  // highest neighbor
+    // for(Point_index k : ngb)
+    for (auto k_py : ngb) {
+      Point_index k = rorder[getint(k_py)];
+      if (k >= i || k < 0)  // ???
+        continue;
+      if (k < j) j = k;
+      Cluster_index rk = raw_cluster[k];
+      adj_clusters.emplace(ds.find_set(rk), rk);
+      // does not insert if ck=ds.find_set(rk) already seen
+      // which rk we keep from those with the same ck is arbitrary
+    }
+    assert((Point_index)raw_cluster.size() == i);
+    if (i == j) {  // local maximum -> new cluster
+      Cluster_index c = n_raw_clusters++;
+      ds_base.emplace_back();  // could be integrated in ds_data, but then we would check the size for every access
+      ds.make_set(c);
+      ds_base[c].max = i;  // max
+      raw_cluster.push_back(c);
+      continue;
+    } else {  // add i to the cluster of j
+      assert(j < i);
+      raw_cluster.push_back(raw_cluster[j]);
+      // FIXME: we are adding point i to the raw cluster of j, but that one might not be in adj_clusters, so we may
+      // merge clusters A and B through a point of C. It is strange, but I don't know if it can really cause problems.
+      // We could just not set j at all and use arbitrarily the first element of adj_clusters.
+    }
+    // possibly merge clusters
+    // we could sort, in case there are several merges, but that doesn't seem so useful
+    Cluster_index rj = raw_cluster[j];
+    Cluster_index cj = ds.find_set(rj);
+    Cluster_index orig_cj = cj;
+    for (auto ckk : adj_clusters) {
+      Cluster_index rk = ckk.second;
+      Cluster_index ck = ckk.first;
+      if (ck == orig_cj) continue;
+      assert(ck == ds.find_set(rk));
+      Point_index j = ds_base[cj].max;
+      Point_index k = ds_base[ck].max;
+      Point_index young = std::max(j, k);
+      Point_index old = std::min(j, k);
+      auto d_young = density[order[young]];
+      auto d_i = density[order[i]];
+      assert(d_young >= d_i);
+      // Always merge (the non-hierarchical algorithm would only conditionally merge here
+      persistence.push_back({d_young, d_i});
+      assert(ds.find_set(rj) != ds.find_set(rk));
+      ds.link(cj, ck);
+      cj = ds.find_set(cj);
+      ds_base[cj].max = old;  // just one parent, no need for find_set
+      // record the raw clusters, we don't know what will have already been merged.
+      merges.push_back({rj, rk, d_young - d_i});
+    }
+  }
+  {
+    boost::counting_iterator<int> b(0), e(ds_base.size());
+    ds.compress_sets(b, e);
+    // Now we stop using find_sets and look at the parent directly
+    // rank is reused to rename clusters contiguously 0, 1, etc
+  }
+  // Maximum for each connected component
+  std::vector<double> max_cc;
+  for (Cluster_index i = 0; i < n_raw_clusters; ++i) {
+    if (ds_base[i].parent == i) max_cc.push_back(density[order[ds_base[i].max]]);
+  }
+  assert((Cluster_index)(merges.size() + max_cc.size()) == n_raw_clusters);
+
+  // TODO: create a "noise" cluster, merging all those not prominent enough?
+
+  // Replay the merges, in increasing order of prominence, to build the hierarchy
+  std::sort(merges.begin(), merges.end(), [](Merge const& a, Merge const& b) { return a.persist < b.persist; });
+  std::vector<std::array<Cluster_index, 2>> children;
+  children.reserve(merges.size());
+  {
+    struct Dat {
+      Cluster_index parent;
+      int rank;
+      Cluster_index name;
+    };
+    std::vector<Dat> ds_bas(2 * n_raw_clusters - 1);
+    Cluster_index i;
+    auto ds_dat =
+        boost::make_function_property_map<std::size_t>([&ds_bas](std::size_t n) -> Dat& { return ds_bas[n]; });
+    auto ds_par = boost::make_transform_value_property_map([](auto& p) -> Cluster_index& { return p.parent; }, ds_dat);
+    auto ds_ran = boost::make_transform_value_property_map([](auto& p) -> int& { return p.rank; }, ds_dat);
+    boost::disjoint_sets<decltype(ds_ran), decltype(ds_par)> ds(ds_ran, ds_par);
+    for (i = 0; i < n_raw_clusters; ++i) {
+      ds.make_set(i);
+      ds_bas[i].name = i;
+    }
+    for (Merge const& m : merges) {
+      Cluster_index j = ds.find_set(m.first);
+      Cluster_index k = ds.find_set(m.second);
+      assert(j != k);
+      children.push_back({ds_bas[j].name, ds_bas[k].name});
+      ds.make_set(i);
+      ds.link(i, j);
+      ds.link(i, k);
+      ds_bas[ds.find_set(i)].name = i;
+      ++i;
+    }
+  }
+
+  std::vector<Cluster_index> raw_cluster_ordered(num_points);
+  for (int i = 0; i < num_points; ++i) raw_cluster_ordered[i] = raw_cluster[rorder[i]];
+  // return raw_cluster, children, persistence
+  // TODO avoid copies: https://github.com/pybind/pybind11/issues/1042
+  return py::make_tuple(py::array(raw_cluster_ordered.size(), raw_cluster_ordered.data()),
+                        py::array(children.size(), children.data()), py::array(persistence.size(), persistence.data()),
+                        py::array(max_cc.size(), max_cc.data()));
+}
+
+auto merge(py::array_t<Cluster_index, py::array::c_style> children, Cluster_index n_leaves, Cluster_index n_final) {
+  if (n_final > n_leaves) {
+    std::cerr << "The number of clusters required " << n_final << " is larger than the number of mini-clusters " << n_leaves << '\n';
+    n_final = n_leaves; // or return something special and let Tomato use leaf_labels_?
+  }
+  py::buffer_info cbuf = children.request();
+  if ((cbuf.ndim != 2 || cbuf.shape[1] != 2) && (cbuf.ndim != 1 || cbuf.shape[0] != 0))
+    throw std::runtime_error("internal error: children have to be (n,2) or empty");
+  const int n_merges = cbuf.shape[0];
+  Cluster_index* d = (Cluster_index*)cbuf.ptr;
+  if (n_merges + n_final < n_leaves) {
+    std::cerr << "The number of clusters required " << n_final << " is smaller than the number of connected components " << n_leaves - n_merges << '\n';
+    n_final = n_leaves - n_merges;
+  }
+  struct Dat {
+    Cluster_index parent;
+    int rank;
+    int name;
+  };
+  std::vector<Dat> ds_bas(2 * n_leaves - 1);
+  auto ds_dat = boost::make_function_property_map<std::size_t>([&ds_bas](std::size_t n) -> Dat& { return ds_bas[n]; });
+  auto ds_par = boost::make_transform_value_property_map([](auto& p) -> Cluster_index& { return p.parent; }, ds_dat);
+  auto ds_ran = boost::make_transform_value_property_map([](auto& p) -> int& { return p.rank; }, ds_dat);
+  boost::disjoint_sets<decltype(ds_ran), decltype(ds_par)> ds(ds_ran, ds_par);
+  Cluster_index i;
+  for (i = 0; i < n_leaves; ++i) {
+    ds.make_set(i);
+    ds_bas[i].name = -1;
+  }
+  for (Cluster_index m = 0; m < n_leaves - n_final; ++m) {
+    Cluster_index j = ds.find_set(d[2 * m]);
+    Cluster_index k = ds.find_set(d[2 * m + 1]);
+    assert(j != k);
+    ds.make_set(i);
+    ds.link(i, j);
+    ds.link(i, k);
+    ++i;
+  }
+  Cluster_index next_cluster_name = 0;
+  std::vector<Cluster_index> ret;
+  ret.reserve(n_leaves);
+  for (Cluster_index j = 0; j < n_leaves; ++j) {
+    Cluster_index k = ds.find_set(j);
+    if (ds_bas[k].name == -1) ds_bas[k].name = next_cluster_name++;
+    ret.push_back(ds_bas[k].name);
+  }
+  return py::array(ret.size(), ret.data());
+}
+
+// TODO: Do a special version when ngb is a numpy array, where we can cast to int[k][n] ?
+// py::isinstance<py::array_t<std::int32_t>> (ou py::isinstance<py::array> et tester dtype) et flags&c_style
+// ou overload (en virant forcecast?)
+// aussi le faire au cas où on n'aurait pas un tableau, mais où chaque liste de voisins serait un tableau ?
+auto hierarchy(py::handle ngb, py::array_t<double, py::array::c_style | py::array::forcecast> density) {
+  // used to be py::iterable ngb, but that's inconvenient if it doesn't come pre-sorted
+  // use py::handle and check if [] (aka __getitem__) works? But then we need to build an object to pass it to []
+  // (I _think_ handle is ok and we don't need object here)
+  py::buffer_info wbuf = density.request();
+  if (wbuf.ndim != 1) throw std::runtime_error("density must be 1D");
+  const int n = wbuf.shape[0];
+  double* d = (double*)wbuf.ptr;
+  // Vector { 0, 1, ..., n-1 }
+  std::vector<Point_index> order(boost::counting_iterator<Point_index>(0), boost::counting_iterator<Point_index>(n));
+  // Permutation of the indices to get points in decreasing order of density
+  std::sort(std::begin(order), std::end(order), [=](Point_index i, Point_index j) { return d[i] > d[j]; });
+  // Inverse permutation
+  std::vector<Point_index> rorder(n);
+  for (Point_index i : boost::irange(0, n)) rorder[order[i]] = i;
+  // Used as:
+  // order[i] is the index of the point with i-th largest density
+  // rorder[i] is the rank of the i-th point in order of decreasing density
+  // TODO: put a wrapper on ngb and d so we don't need to pass (r)order (there is still the issue of reordering the
+  // output)
+  return tomato(n, ngb, d, order, rorder);
+}
+
+PYBIND11_MODULE(_tomato, m) {
+  m.doc() = "Internals of tomato clustering";
+  m.def("hierarchy", &hierarchy, "does the clustering");
+  m.def("merge", &merge, "merge clusters");
+}
diff --git a/src/python/gudhi/clustering/tomato.py b/src/python/gudhi/clustering/tomato.py
new file mode 100644
index 00000000..fbba3cc8
--- /dev/null
+++ b/src/python/gudhi/clustering/tomato.py
@@ -0,0 +1,321 @@
+# 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):       Marc Glisse
+#
+# Copyright (C) 2020 Inria
+#
+# Modification(s):
+#   - YYYY/MM Author: Description of the modification
+
+import numpy
+from ..point_cloud.knn import KNearestNeighbors
+from ..point_cloud.dtm import DTMDensity
+from ._tomato import *
+
+# The fit/predict interface is not so well suited...
+
+
+class Tomato:
+    """
+    This clustering algorithm needs a neighborhood graph on the points, and an estimation of the density at each point.
+    A few possible graph constructions and density estimators are provided for convenience, but it is perfectly natural
+    to provide your own.
+
+    :Requires: `SciPy <installation.html#scipy>`_, `Scikit-learn <installation.html#scikit-learn>`_ or others
+        (see :class:`~gudhi.point_cloud.knn.KNearestNeighbors`) in function of the options.
+
+    Attributes
+    ----------
+    n_clusters_: int
+        The number of clusters. Writing to it automatically adjusts `labels_`.
+    merge_threshold_: float
+        minimum prominence of a cluster so it doesn't get merged. Writing to it automatically adjusts `labels_`.
+    n_leaves_: int
+        number of leaves (unstable clusters) in the hierarchical tree
+    leaf_labels_: ndarray of shape (n_samples,)
+        cluster labels for each point, at the very bottom of the hierarchy
+    labels_: ndarray of shape (n_samples,)
+        cluster labels for each point, after merging
+    diagram_: ndarray of shape (`n_leaves_`, 2)
+        persistence diagram (only the finite points)
+    max_weight_per_cc_: ndarray of shape (n_connected_components,)
+        maximum of the density function on each connected component. This corresponds to the abscissa of infinite
+        points in the diagram
+    children_: ndarray of shape (`n_leaves_`-n_connected_components, 2)
+        The children of each non-leaf node. Values less than `n_leaves_` correspond to leaves of the tree.
+        A node i greater than or equal to `n_leaves_` is a non-leaf node and has children children_[i - `n_leaves_`].
+        Alternatively at the i-th iteration, children[i][0] and children[i][1] are merged to form node `n_leaves_` + i
+    weights_: ndarray of shape (n_samples,)
+        weights of the points, as computed by the density estimator or provided by the user
+    params_: dict
+        Parameters like metric, etc
+    """
+
+    def __init__(
+        self,
+        graph_type="knn",
+        density_type="logDTM",
+        n_clusters=None,
+        merge_threshold=None,
+        #       eliminate_threshold=None,
+        #           eliminate_threshold (float): minimum max weight of a cluster so it doesn't get eliminated
+        **params
+    ):
+        """
+        Args:
+            graph_type (str): 'manual', 'knn' or 'radius'. Default is 'knn'.
+            density_type (str): 'manual', 'DTM', 'logDTM', 'KDE' or 'logKDE'. When you have many points,
+                'KDE' and 'logKDE' tend to be slower. Default is 'logDTM'.
+            metric (str|Callable): metric used when calculating the distance between instances in a feature array.
+                Defaults to Minkowski of parameter p.
+            kde_params (dict): if density_type is 'KDE' or 'logKDE', additional parameters passed directly to
+                sklearn.neighbors.KernelDensity.
+            k (int): number of neighbors for a knn graph (including the vertex itself). Defaults to 10.
+            k_DTM (int): number of neighbors for the DTM density estimation (including the vertex itself).
+                Defaults to k.
+            r (float): size of a neighborhood if graph_type is 'radius'. Also used as default bandwidth in kde_params.
+            eps (float): (1+eps) approximation factor when computing distances (ignored in many cases).
+            n_clusters (int): number of clusters requested. Defaults to None, i.e. no merging occurs and we get
+                the maximal number of clusters.
+            merge_threshold (float): minimum prominence of a cluster so it doesn't get merged.
+            symmetrize_graph (bool): whether we should add edges to make the neighborhood graph symmetric.
+                This can be useful with k-NN for small k. Defaults to false.
+            p (float): norm L^p on input points. Defaults to 2.
+            q (float): order used to compute the distance to measure. Defaults to dim.
+                Beware that when the dimension is large, this can easily cause overflows.
+            dim (float): final exponent in DTM density estimation, representing the dimension. Defaults to the
+                dimension, or 2 when the dimension cannot be read from the input (metric is "precomputed").
+            n_jobs (int): Number of jobs to schedule for parallel processing on the CPU.
+                If -1 is given all processors are used. Default: 1.
+            params: extra parameters are passed to :class:`~gudhi.point_cloud.knn.KNearestNeighbors` and
+                :class:`~gudhi.point_cloud.dtm.DTMDensity`.
+        """
+        # Should metric='precomputed' mean input_type='distance_matrix'?
+        # Should we be able to pass metric='minkowski' (what None does currently)?
+        self.graph_type_ = graph_type
+        self.density_type_ = density_type
+        self.params_ = params
+        self.__n_clusters = n_clusters
+        self.__merge_threshold = merge_threshold
+        # self.eliminate_threshold_ = eliminate_threshold
+        if n_clusters and merge_threshold:
+            raise ValueError("Cannot specify both a merge threshold and a number of clusters")
+
+    def fit(self, X, y=None, weights=None):
+        """
+        Args:
+            X ((n,d)-array of float|(n,n)-array of float|Sequence[Iterable[int]]): coordinates of the points,
+                or distance matrix (full, not just a triangle) if metric is "precomputed", or list of neighbors
+                for each point (points are represented by their index, starting from 0) if graph_type is "manual".
+                The number of points is currently limited to about 2 billion.
+            weights (ndarray of shape (n_samples)): if density_type is 'manual', a density estimate at each point
+            y: Not used, present here for API consistency with scikit-learn by convention.
+        """
+        # TODO: First detect if this is a new call with the same data (only threshold changed?)
+        # TODO: less code duplication (subroutines?), less spaghetti, but don't compute neighbors twice if not needed. Clear error message for missing or contradictory parameters.
+        if weights is not None:
+            density_type = "manual"
+        else:
+            density_type = self.density_type_
+            if density_type == "manual":
+                raise ValueError("If density_type is 'manual', you must provide weights to fit()")
+
+        if self.graph_type_ == "manual":
+            self.neighbors_ = X
+            # FIXME: uniformize "message 'option'" vs 'message "option"'
+            assert density_type == "manual", 'If graph_type is "manual", density_type must be as well'
+        else:
+            metric = self.params_.get("metric", "minkowski")
+            if metric != "precomputed":
+                self.points_ = X
+
+        # Slight complication to avoid computing knn twice.
+        need_knn = 0
+        need_knn_ngb = False
+        need_knn_dist = False
+        if self.graph_type_ == "knn":
+            k_graph = self.params_.get("k", 10)
+            # If X has fewer than k points...
+            if k_graph > len(X):
+                k_graph = len(X)
+            need_knn = k_graph
+            need_knn_ngb = True
+        if self.density_type_ in ["DTM", "logDTM"]:
+            k = self.params_.get("k", 10)
+            k_DTM = self.params_.get("k_DTM", k)
+            # If X has fewer than k points...
+            if k_DTM > len(X):
+                k_DTM = len(X)
+            need_knn = max(need_knn, k_DTM)
+            need_knn_dist = True
+            # if we ask for more neighbors for the graph than the DTM, getting the distances is a slight waste,
+            # but it looks negligible
+        if need_knn > 0:
+            knn_args = dict(self.params_)
+            knn_args["k"] = need_knn
+            knn = KNearestNeighbors(return_index=need_knn_ngb, return_distance=need_knn_dist, **knn_args).fit_transform(
+                X
+            )
+            if need_knn_ngb:
+                if need_knn_dist:
+                    self.neighbors_ = knn[0][:, 0:k_graph]
+                    knn_dist = knn[1]
+                else:
+                    self.neighbors_ = knn
+            elif need_knn_dist:
+                knn_dist = knn
+        if self.density_type_ in ["DTM", "logDTM"]:
+            dim = self.params_.get("dim")
+            if dim is None:
+                dim = len(X[0]) if metric != "precomputed" else 2
+            q = self.params_.get("q", dim)
+            weights = DTMDensity(k=k_DTM, metric="neighbors", dim=dim, q=q).fit_transform(knn_dist)
+            if self.density_type_ == "logDTM":
+                weights = numpy.log(weights)
+
+        if self.graph_type_ == "radius":
+            if metric in ["minkowski", "euclidean", "manhattan", "chebyshev"]:
+                from scipy.spatial import cKDTree
+
+                tree = cKDTree(X)
+                # TODO: handle "l1" and "l2" aliases?
+                p = self.params_.get("p")
+                if metric == "euclidean":
+                    assert p is None or p == 2, "p=" + str(p) + " is not consistent with metric='euclidean'"
+                    p = 2
+                elif metric == "manhattan":
+                    assert p is None or p == 1, "p=" + str(p) + " is not consistent with metric='manhattan'"
+                    p = 1
+                elif metric == "chebyshev":
+                    assert p is None or p == numpy.inf, "p=" + str(p) + " is not consistent with metric='chebyshev'"
+                    p = numpy.inf
+                elif p is None:
+                    p = 2  # the default
+                eps = self.params_.get("eps", 0)
+                self.neighbors_ = tree.query_ball_tree(tree, r=self.params_["r"], p=p, eps=eps)
+
+            # TODO: sklearn's NearestNeighbors.radius_neighbors can handle more metrics efficiently via its BallTree
+            # (don't bother with the _graph variant, it just calls radius_neighbors).
+            elif metric != "precomputed":
+                from sklearn.metrics import pairwise_distances
+
+                X = pairwise_distances(X, metric=metric, n_jobs=self.params_.get("n_jobs"))
+                metric = "precomputed"
+
+            if metric == "precomputed":
+                # TODO: parallelize? May not be worth it.
+                X = numpy.asarray(X)
+                r = self.params_["r"]
+                self.neighbors_ = [numpy.flatnonzero(l <= r) for l in X]
+
+        if self.density_type_ in {"KDE", "logKDE"}:
+            # Slow...
+            assert (
+                self.graph_type_ != "manual" and metric != "precomputed"
+            ), "Scikit-learn's KernelDensity requires point coordinates"
+            kde_params = dict(self.params_.get("kde_params", dict()))
+            kde_params.setdefault("metric", metric)
+            r = self.params_.get("r")
+            if r is not None:
+                kde_params.setdefault("bandwidth", r)
+            # Should we default rtol to eps?
+            from sklearn.neighbors import KernelDensity
+
+            weights = KernelDensity(**kde_params).fit(self.points_).score_samples(self.points_)
+            if self.density_type_ == "KDE":
+                weights = numpy.exp(weights)
+
+        # TODO: do it at the C++ level and/or in parallel if this is too slow?
+        if self.params_.get("symmetrize_graph"):
+            self.neighbors_ = [set(line) for line in self.neighbors_]
+            for i, line in enumerate(self.neighbors_):
+                line.discard(i)
+                for j in line:
+                    self.neighbors_[j].add(i)
+
+        self.weights_ = weights
+        # This is where the main computation happens
+        self.leaf_labels_, self.children_, self.diagram_, self.max_weight_per_cc_ = hierarchy(self.neighbors_, weights)
+        self.n_leaves_ = len(self.max_weight_per_cc_) + len(self.children_)
+        assert self.leaf_labels_.max() + 1 == len(self.max_weight_per_cc_) + len(self.children_)
+        # TODO: deduplicate this code with the setters below
+        if self.__merge_threshold:
+            assert not self.__n_clusters
+            self.__n_clusters = numpy.count_nonzero(
+                self.diagram_[:, 0] - self.diagram_[:, 1] > self.__merge_threshold
+            ) + len(self.max_weight_per_cc_)
+        if self.__n_clusters:
+            # TODO: set corresponding merge_threshold?
+            renaming = merge(self.children_, self.n_leaves_, self.__n_clusters)
+            self.labels_ = renaming[self.leaf_labels_]
+            # In case the user asked for something impossible.
+            # TODO: check for impossible situations before calling merge.
+            self.__n_clusters = self.labels_.max() + 1
+        else:
+            self.labels_ = self.leaf_labels_
+            self.__n_clusters = self.n_leaves_
+        return self
+
+    def fit_predict(self, X, y=None, weights=None):
+        """
+        Equivalent to fit(), and returns the `labels_`.
+        """
+        return self.fit(X, y, weights).labels_
+
+    # TODO: add argument k or threshold? Have a version where you can click and it shows the line and the corresponding k?
+    def plot_diagram(self):
+        """
+        """
+        import matplotlib.pyplot as plt
+
+        l = self.max_weight_per_cc_.min()
+        r = self.max_weight_per_cc_.max()
+        if self.diagram_.size > 0:
+            plt.plot(self.diagram_[:, 0], self.diagram_[:, 1], "ro")
+            l = min(l, self.diagram_[:, 1].min())
+            r = max(r, self.diagram_[:, 0].max())
+        if l == r:
+            if l > 0:
+                l, r = 0.9 * l, 1.1 * r
+            elif l < 0:
+                l, r = 1.1 * l, 0.9 * r
+            else:
+                l, r = -1.0, 1.0
+        plt.plot([l, r], [l, r])
+        plt.plot(
+            self.max_weight_per_cc_, numpy.full(self.max_weight_per_cc_.shape, 1.1 * l - 0.1 * r), "ro", color="green"
+        )
+        plt.show()
+
+    # Use set_params instead?
+    @property
+    def n_clusters_(self):
+        return self.__n_clusters
+
+    @n_clusters_.setter
+    def n_clusters_(self, n_clusters):
+        if n_clusters == self.__n_clusters:
+            return
+        self.__n_clusters = n_clusters
+        self.__merge_threshold = None
+        if hasattr(self, "leaf_labels_"):
+            renaming = merge(self.children_, self.n_leaves_, self.__n_clusters)
+            self.labels_ = renaming[self.leaf_labels_]
+            # In case the user asked for something impossible
+            self.__n_clusters = self.labels_.max() + 1
+
+    @property
+    def merge_threshold_(self):
+        return self.__merge_threshold
+
+    @merge_threshold_.setter
+    def merge_threshold_(self, merge_threshold):
+        if merge_threshold == self.__merge_threshold:
+            return
+        if hasattr(self, "leaf_labels_"):
+            self.n_clusters_ = numpy.count_nonzero(self.diagram_[:, 0] - self.diagram_[:, 1] > merge_threshold) + len(
+                self.max_weight_per_cc_
+            )
+        else:
+            self.__n_clusters = None
+        self.__merge_threshold = merge_threshold
diff --git a/src/python/gudhi/persistence_graphical_tools.py b/src/python/gudhi/persistence_graphical_tools.py
index 6a74a6ca..c6766c70 100644
--- a/src/python/gudhi/persistence_graphical_tools.py
+++ b/src/python/gudhi/persistence_graphical_tools.py
@@ -11,6 +11,7 @@
 from os import path
 from math import isfinite
 import numpy as np
+from functools import lru_cache
 
 from gudhi.reader_utils import read_persistence_intervals_in_dimension
 from gudhi.reader_utils import read_persistence_intervals_grouped_by_dimension
@@ -56,6 +57,17 @@ def _array_handler(a):
     else:
         return a
 
+@lru_cache(maxsize=1)
+def _matplotlib_can_use_tex():
+    """This function returns True if matplotlib can deal with LaTeX, False otherwise.
+    The returned value is cached.
+    """
+    try:
+        from matplotlib import checkdep_usetex
+        return checkdep_usetex(True)
+    except ImportError:
+        print("This function is not available, you may be missing matplotlib.")
+
 
 def plot_persistence_barcode(
     persistence=[],
@@ -105,9 +117,10 @@ def plot_persistence_barcode(
     try:
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
-        from matplotlib import rc
-        plt.rc('text', usetex=True)
-        plt.rc('font', family='serif')
+        if _matplotlib_can_use_tex():
+            from matplotlib import rc
+            plt.rc('text', usetex=True)
+            plt.rc('font', family='serif')
 
         if persistence_file != "":
             if path.isfile(persistence_file):
@@ -250,9 +263,10 @@ def plot_persistence_diagram(
     try:
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
-        from matplotlib import rc
-        plt.rc('text', usetex=True)
-        plt.rc('font', family='serif')
+        if _matplotlib_can_use_tex():
+            from matplotlib import rc
+            plt.rc('text', usetex=True)
+            plt.rc('font', family='serif')
 
         if persistence_file != "":
             if path.isfile(persistence_file):
@@ -422,9 +436,10 @@ def plot_persistence_density(
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
         from scipy.stats import kde
-        from matplotlib import rc
-        plt.rc('text', usetex=True)
-        plt.rc('font', family='serif')
+        if _matplotlib_can_use_tex():
+            from matplotlib import rc
+            plt.rc('text', usetex=True)
+            plt.rc('font', family='serif')
 
         if persistence_file != "":
             if dimension is None:
diff --git a/src/python/gudhi/representations/metrics.py b/src/python/gudhi/representations/metrics.py
index cf2e0879..142ddef1 100644
--- a/src/python/gudhi/representations/metrics.py
+++ b/src/python/gudhi/representations/metrics.py
@@ -350,23 +350,30 @@ class PersistenceFisherDistance(BaseEstimator, TransformerMixin):
         """
         return _persistence_fisher_distance(diag1, diag2, bandwidth=self.bandwidth, kernel_approx=self.kernel_approx)
 
+
 class WassersteinDistance(BaseEstimator, TransformerMixin):
     """
     This is a class for computing the Wasserstein distance matrix from a list of persistence diagrams. 
     """
-    def __init__(self, order=2, internal_p=2, mode="pot", delta=0.01, n_jobs=None):
+
+    def __init__(self, order=1, internal_p=np.inf, mode="hera", delta=0.01, n_jobs=None):
         """
         Constructor for the WassersteinDistance class.
 
         Parameters:
-            order (int): exponent for Wasserstein, default value is 2., see :func:`gudhi.wasserstein.wasserstein_distance`.
-            internal_p (int): ground metric on the (upper-half) plane (i.e. norm l_p in R^2), default value is 2 (euclidean norm), see :func:`gudhi.wasserstein.wasserstein_distance`.
-            mode (str): method for computing Wasserstein distance. Either "pot" or "hera".
+            order (int): exponent for Wasserstein, default value is 1., see :func:`gudhi.wasserstein.wasserstein_distance`.
+            internal_p (int): ground metric on the (upper-half) plane (i.e. norm l_p in R^2), default value is `np.inf`, see :func:`gudhi.wasserstein.wasserstein_distance`.
+            mode (str): method for computing Wasserstein distance. Either "pot" or "hera". Default set to "hera".
             delta (float): relative error 1+delta. Used only if mode == "hera".
             n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_distances` for details.
         """
         self.order, self.internal_p, self.mode = order, internal_p, mode
-        self.metric = "pot_wasserstein" if mode == "pot" else "hera_wasserstein"
+        if mode == "pot":
+            self.metric = "pot_wasserstein"
+        elif mode == "hera":
+            self.metric = "hera_wasserstein"
+        else:
+            raise NameError("Unknown mode. Current available values for mode are 'hera' and 'pot'")
         self.delta = delta
         self.n_jobs = n_jobs
 
diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx
index 9cb24221..20e66d9f 100644
--- a/src/python/gudhi/simplex_tree.pyx
+++ b/src/python/gudhi/simplex_tree.pyx
@@ -225,13 +225,12 @@ cdef class SimplexTree:
             preincrement(it)
 
     def get_skeleton(self, dimension):
-        """This function returns the (simplices of the) skeleton of a maximum
-        given dimension.
+        """This function returns a generator with the (simplices of the) skeleton of a maximum given dimension.
 
         :param dimension: The skeleton dimension value.
         :type dimension: int.
         :returns:  The (simplices of the) skeleton of a maximum dimension.
-        :rtype:  list of tuples(simplex, filtration)
+        :rtype:  generator with tuples(simplex, filtration)
         """
         cdef Simplex_tree_skeleton_iterator it = self.get_ptr().get_skeleton_iterator_begin(dimension)
         cdef Simplex_tree_skeleton_iterator end = self.get_ptr().get_skeleton_iterator_end(dimension)
diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py
index 89ecab1c..b37d30bb 100644
--- a/src/python/gudhi/wasserstein/wasserstein.py
+++ b/src/python/gudhi/wasserstein/wasserstein.py
@@ -73,8 +73,8 @@ def _perstot_autodiff(X, order, internal_p):
 def _perstot(X, order, internal_p, enable_autodiff):
     '''
     :param X: (n x 2) numpy.array (points of a given diagram).
-    :param order: exponent for Wasserstein. Default value is 2.
-    :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); Default value is 2 (Euclidean norm).
+    :param order: exponent for Wasserstein.
+    :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2).
     :param enable_autodiff: If X is torch.tensor, tensorflow.Tensor or jax.numpy.ndarray, make the computation
         transparent to automatic differentiation.
     :type enable_autodiff: bool
@@ -88,7 +88,7 @@ def _perstot(X, order, internal_p, enable_autodiff):
         return np.linalg.norm(_dist_to_diag(X, internal_p), ord=order)
 
 
-def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2., enable_autodiff=False):
+def wasserstein_distance(X, Y, matching=False, order=1., internal_p=np.inf, enable_autodiff=False):
     '''
     :param X: (n x 2) numpy.array encoding the (finite points of the) first diagram. Must not contain essential points
                 (i.e. with infinite coordinate).
@@ -96,9 +96,9 @@ def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2., enable_a
     :param matching: if True, computes and returns the optimal matching between X and Y, encoded as
                      a (n x 2) np.array  [...[i,j]...], meaning the i-th point in X is matched to
                      the j-th point in Y, with the convention (-1) represents the diagonal.
-    :param order: exponent for Wasserstein; Default value is 2.
+    :param order: exponent for Wasserstein; Default value is 1.
     :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2);
-                       Default value is 2 (Euclidean norm).
+                       Default value is `np.inf`.
     :param enable_autodiff: If X and Y are torch.tensor, tensorflow.Tensor or jax.numpy.ndarray, make the computation
         transparent to automatic differentiation. This requires the package EagerPy and is currently incompatible
         with `matching=True`.
diff --git a/src/python/include/Alpha_complex_factory.h b/src/python/include/Alpha_complex_factory.h
new file mode 100644
index 00000000..d699ad9b
--- /dev/null
+++ b/src/python/include/Alpha_complex_factory.h
@@ -0,0 +1,139 @@
+/*    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) 2020 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef INCLUDE_ALPHA_COMPLEX_FACTORY_H_
+#define INCLUDE_ALPHA_COMPLEX_FACTORY_H_
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Alpha_complex.h>
+#include <gudhi/Alpha_complex_3d.h>
+#include <gudhi/Alpha_complex_options.h>
+#include <CGAL/Epeck_d.h>
+#include <CGAL/Epick_d.h>
+
+#include <boost/range/adaptor/transformed.hpp>
+
+#include "Simplex_tree_interface.h"
+
+#include <iostream>
+#include <vector>
+#include <string>
+#include <memory>  // for std::unique_ptr
+
+namespace Gudhi {
+
+namespace alpha_complex {
+
+template <typename CgalPointType>
+std::vector<double> pt_cgal_to_cython(CgalPointType const& point) {
+  std::vector<double> vd;
+  vd.reserve(point.dimension());
+  for (auto coord = point.cartesian_begin(); coord != point.cartesian_end(); coord++)
+    vd.push_back(CGAL::to_double(*coord));
+  return vd;
+}
+
+template <typename CgalPointType>
+static CgalPointType pt_cython_to_cgal(std::vector<double> const& vec) {
+  return CgalPointType(vec.size(), vec.begin(), vec.end());
+}
+
+class Abstract_alpha_complex {
+ public:
+  virtual std::vector<double> get_point(int vh) = 0;
+  virtual bool create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square,
+                                   bool default_filtration_value) = 0;
+};
+
+class Exact_Alphacomplex_dD : public Abstract_alpha_complex {
+ private:
+  using Kernel = CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>;
+  using Point = typename Kernel::Point_d;
+
+ public:
+  Exact_Alphacomplex_dD(const std::vector<std::vector<double>>& points, bool exact_version)
+    : exact_version_(exact_version),
+      alpha_complex_(boost::adaptors::transform(points, pt_cython_to_cgal<Point>)) {
+  }
+
+  virtual std::vector<double> get_point(int vh) override {
+    Point const& point = alpha_complex_.get_point(vh);
+    return pt_cgal_to_cython(point);
+  }
+
+  virtual bool create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square,
+                                   bool default_filtration_value) override {
+    return alpha_complex_.create_complex(*simplex_tree, max_alpha_square, exact_version_, default_filtration_value);
+  }
+
+ private:
+  bool exact_version_;
+  Alpha_complex<Kernel> alpha_complex_;
+};
+
+class Inexact_Alphacomplex_dD : public Abstract_alpha_complex {
+ private:
+  using Kernel = CGAL::Epick_d<CGAL::Dynamic_dimension_tag>;
+  using Point = typename Kernel::Point_d;
+
+ public:
+  Inexact_Alphacomplex_dD(const std::vector<std::vector<double>>& points, bool exact_version)
+    : exact_version_(exact_version),
+      alpha_complex_(boost::adaptors::transform(points, pt_cython_to_cgal<Point>)) {
+  }
+
+  virtual std::vector<double> get_point(int vh) override {
+    Point const& point = alpha_complex_.get_point(vh);
+    return pt_cgal_to_cython(point);
+  }
+  virtual bool create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square,
+                                   bool default_filtration_value) override {
+    return alpha_complex_.create_complex(*simplex_tree, max_alpha_square, exact_version_, default_filtration_value);
+  }
+
+ private:
+  bool exact_version_;
+  Alpha_complex<Kernel> alpha_complex_;
+};
+
+template <complexity Complexity>
+class Alphacomplex_3D : public Abstract_alpha_complex {
+ private:
+  using Point = typename Alpha_complex_3d<Complexity, false, false>::Bare_point_3;
+
+  static Point pt_cython_to_cgal_3(std::vector<double> const& vec) {
+    return Point(vec[0], vec[1], vec[2]);
+  }
+
+ public:
+  Alphacomplex_3D(const std::vector<std::vector<double>>& points)
+    : alpha_complex_(boost::adaptors::transform(points, pt_cython_to_cgal_3)) {
+  }
+
+  virtual std::vector<double> get_point(int vh) override {
+    Point const& point = alpha_complex_.get_point(vh);
+    return pt_cgal_to_cython(point);
+  }
+
+  virtual bool create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square,
+                           bool default_filtration_value) override {
+    return alpha_complex_.create_complex(*simplex_tree, max_alpha_square);
+  }
+
+ private:
+  Alpha_complex_3d<Complexity, false, false> alpha_complex_;
+};
+
+
+}  // namespace alpha_complex
+
+}  // namespace Gudhi
+
+#endif  // INCLUDE_ALPHA_COMPLEX_FACTORY_H_
diff --git a/src/python/include/Alpha_complex_interface.h b/src/python/include/Alpha_complex_interface.h
index 3ac5db1f..23be194d 100644
--- a/src/python/include/Alpha_complex_interface.h
+++ b/src/python/include/Alpha_complex_interface.h
@@ -11,12 +11,8 @@
 #ifndef INCLUDE_ALPHA_COMPLEX_INTERFACE_H_
 #define INCLUDE_ALPHA_COMPLEX_INTERFACE_H_
 
-#include <gudhi/Simplex_tree.h>
-#include <gudhi/Alpha_complex.h>
-#include <CGAL/Epeck_d.h>
-#include <CGAL/Epick_d.h>
-
-#include <boost/range/adaptor/transformed.hpp>
+#include "Alpha_complex_factory.h"
+#include <gudhi/Alpha_complex_options.h>
 
 #include "Simplex_tree_interface.h"
 
@@ -30,67 +26,51 @@ namespace Gudhi {
 namespace alpha_complex {
 
 class Alpha_complex_interface {
- private:
-  using Exact_kernel = CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>;
-  using Inexact_kernel = CGAL::Epick_d<CGAL::Dynamic_dimension_tag>;
-  using Point_exact_kernel = typename Exact_kernel::Point_d;
-  using Point_inexact_kernel = typename Inexact_kernel::Point_d;
-
-  template <typename CgalPointType>
-  std::vector<double> pt_cgal_to_cython(CgalPointType& point) {
-    std::vector<double> vd;
-    for (auto coord = point.cartesian_begin(); coord != point.cartesian_end(); coord++)
-      vd.push_back(CGAL::to_double(*coord));
-    return vd;
-  }
-
-  template <typename CgalPointType>
-  static CgalPointType pt_cython_to_cgal(std::vector<double> const& vec) {
-    return CgalPointType(vec.size(), vec.begin(), vec.end());
-  }
-
  public:
-  Alpha_complex_interface(const std::vector<std::vector<double>>& points, bool fast_version)
-      : fast_version_(fast_version) {
-    if (fast_version_) {
-      ac_inexact_ptr_ = std::make_unique<Alpha_complex<Inexact_kernel>>(
-          boost::adaptors::transform(points, pt_cython_to_cgal<Point_inexact_kernel>));
-    } else {
-      ac_exact_ptr_ = std::make_unique<Alpha_complex<Exact_kernel>>(
-          boost::adaptors::transform(points, pt_cython_to_cgal<Point_exact_kernel>));
-    }
-  }
-
-  Alpha_complex_interface(const std::string& off_file_name, bool fast_version, bool from_file = true)
-      : fast_version_(fast_version) {
-    if (fast_version_)
-      ac_inexact_ptr_ = std::make_unique<Alpha_complex<Inexact_kernel>>(off_file_name);
-    else
-      ac_exact_ptr_ = std::make_unique<Alpha_complex<Exact_kernel>>(off_file_name);
+  Alpha_complex_interface(const std::vector<std::vector<double>>& points, bool fast_version, bool exact_version)
+  : points_(points),
+    fast_version_(fast_version),
+    exact_version_(exact_version) {
   }
 
   std::vector<double> get_point(int vh) {
-    if (fast_version_) {
-      Point_inexact_kernel const& point = ac_inexact_ptr_->get_point(vh);
-      return pt_cgal_to_cython(point);
-    } else {
-      Point_exact_kernel const& point = ac_exact_ptr_->get_point(vh);
-      return pt_cgal_to_cython(point);
-    }
+    return alpha_ptr_->get_point(vh);
   }
 
-  void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square, bool exact_version,
+  void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square,
                            bool default_filtration_value) {
-    if (fast_version_)
-      ac_inexact_ptr_->create_complex(*simplex_tree, max_alpha_square, exact_version, default_filtration_value);
-    else
-      ac_exact_ptr_->create_complex(*simplex_tree, max_alpha_square, exact_version, default_filtration_value);
+    if (points_.size() > 0) {
+      std::size_t dimension = points_[0].size();
+      if (dimension == 3 && !default_filtration_value) {
+        if (fast_version_)
+          alpha_ptr_ = std::make_unique<Alphacomplex_3D<Gudhi::alpha_complex::complexity::FAST>>(points_);
+        else if (exact_version_)
+          alpha_ptr_ = std::make_unique<Alphacomplex_3D<Gudhi::alpha_complex::complexity::EXACT>>(points_);
+        else
+          alpha_ptr_ = std::make_unique<Alphacomplex_3D<Gudhi::alpha_complex::complexity::SAFE>>(points_);
+        if (!alpha_ptr_->create_simplex_tree(simplex_tree, max_alpha_square, default_filtration_value)) {
+          // create_simplex_tree will fail if all points are on a plane - Retry with dD by setting dimension to 2
+          dimension--;
+          alpha_ptr_.reset();
+        }
+      }
+      // Not ** else ** because we have to take into account if 3d fails
+      if (dimension != 3 || default_filtration_value) {
+        if (fast_version_) {
+          alpha_ptr_ = std::make_unique<Inexact_Alphacomplex_dD>(points_, exact_version_);
+        } else {
+          alpha_ptr_ = std::make_unique<Exact_Alphacomplex_dD>(points_, exact_version_);
+        }
+        alpha_ptr_->create_simplex_tree(simplex_tree, max_alpha_square, default_filtration_value);
+      }
+    }
   }
 
  private:
+  std::unique_ptr<Abstract_alpha_complex> alpha_ptr_;
+  std::vector<std::vector<double>> points_;
   bool fast_version_;
-  std::unique_ptr<Alpha_complex<Exact_kernel>> ac_exact_ptr_;
-  std::unique_ptr<Alpha_complex<Inexact_kernel>> ac_inexact_ptr_;
+  bool exact_version_;
 };
 
 }  // namespace alpha_complex
diff --git a/src/python/test/test_alpha_complex.py b/src/python/test/test_alpha_complex.py
index 943ad2c4..a4ee260b 100755
--- a/src/python/test/test_alpha_complex.py
+++ b/src/python/test/test_alpha_complex.py
@@ -8,7 +8,7 @@
       - YYYY/MM Author: Description of the modification
 """
 
-from gudhi import AlphaComplex, SimplexTree
+import gudhi as gd
 import math
 import numpy as np
 import pytest
@@ -25,17 +25,16 @@ __license__ = "MIT"
 
 
 def _empty_alpha(precision):
-    alpha_complex = AlphaComplex(points=[[0, 0]], precision = precision)
+    alpha_complex = gd.AlphaComplex(points=[[0, 0]], precision = precision)
     assert alpha_complex.__is_defined() == True
 
 def test_empty_alpha():
-    _empty_alpha('fast')
-    _empty_alpha('safe')
-    _empty_alpha('exact')
+    for precision in ['fast', 'safe', 'exact']:
+        _empty_alpha(precision)
 
 def _infinite_alpha(precision):
     point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
-    alpha_complex = AlphaComplex(points=point_list, precision = precision)
+    alpha_complex = gd.AlphaComplex(points=point_list, precision = precision)
     assert alpha_complex.__is_defined() == True
 
     simplex_tree = alpha_complex.create_simplex_tree()
@@ -84,13 +83,12 @@ def _infinite_alpha(precision):
         assert False
 
 def test_infinite_alpha():
-    _infinite_alpha('fast')
-    _infinite_alpha('safe')
-    _infinite_alpha('exact')
+    for precision in ['fast', 'safe', 'exact']:
+        _infinite_alpha(precision)
 
 def _filtered_alpha(precision):
     point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
-    filtered_alpha = AlphaComplex(points=point_list, precision = precision)
+    filtered_alpha = gd.AlphaComplex(points=point_list, precision = precision)
 
     simplex_tree = filtered_alpha.create_simplex_tree(max_alpha_square=0.25)
 
@@ -128,9 +126,8 @@ def _filtered_alpha(precision):
     assert simplex_tree.get_cofaces([0], 1) == [([0, 1], 0.25), ([0, 2], 0.25)]
 
 def test_filtered_alpha():
-    _filtered_alpha('fast')
-    _filtered_alpha('safe')
-    _filtered_alpha('exact')
+    for precision in ['fast', 'safe', 'exact']:
+        _filtered_alpha(precision)
 
 def _safe_alpha_persistence_comparison(precision):
     #generate periodic signal
@@ -144,10 +141,10 @@ def _safe_alpha_persistence_comparison(precision):
     embedding2 = [[signal[i], delayed[i]] for i in range(len(time))]
     
     #build alpha complex and simplex tree
-    alpha_complex1 = AlphaComplex(points=embedding1, precision = precision)
+    alpha_complex1 = gd.AlphaComplex(points=embedding1, precision = precision)
     simplex_tree1 = alpha_complex1.create_simplex_tree()
     
-    alpha_complex2 = AlphaComplex(points=embedding2, precision = precision)
+    alpha_complex2 = gd.AlphaComplex(points=embedding2, precision = precision)
     simplex_tree2 = alpha_complex2.create_simplex_tree()
     
     diag1 = simplex_tree1.persistence()
@@ -165,7 +162,7 @@ def test_safe_alpha_persistence_comparison():
 
 def _delaunay_complex(precision):
     point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
-    filtered_alpha = AlphaComplex(points=point_list, precision = precision)
+    filtered_alpha = gd.AlphaComplex(points=point_list, precision = precision)
 
     simplex_tree = filtered_alpha.create_simplex_tree(default_filtration_value = True)
 
@@ -197,6 +194,54 @@ def _delaunay_complex(precision):
         assert math.isnan(filtered_value[1])
 
 def test_delaunay_complex():
-    _delaunay_complex('fast')
-    _delaunay_complex('safe')
-    _delaunay_complex('exact')
+    for precision in ['fast', 'safe', 'exact']:
+        _delaunay_complex(precision)
+
+def _3d_points_on_a_plane(precision, default_filtration_value):
+    alpha = gd.AlphaComplex(off_file=gd.__root_source_dir__ + '/data/points/alphacomplexdoc.off',
+                         precision = precision)
+
+    simplex_tree = alpha.create_simplex_tree(default_filtration_value = default_filtration_value)
+    assert simplex_tree.dimension() == 2
+    assert simplex_tree.num_vertices() == 7
+    assert simplex_tree.num_simplices() == 25
+
+def test_3d_points_on_a_plane():
+    for default_filtration_value in [True, False]:
+        for precision in ['fast', 'safe', 'exact']:
+            _3d_points_on_a_plane(precision, default_filtration_value)
+
+def _3d_tetrahedrons(precision):
+    points = 10*np.random.rand(10, 3)
+    alpha = gd.AlphaComplex(points=points, precision = precision)
+    st_alpha = alpha.create_simplex_tree(default_filtration_value = False)
+    # New AlphaComplex for get_point to work
+    delaunay = gd.AlphaComplex(points=points, precision = precision)
+    st_delaunay = delaunay.create_simplex_tree(default_filtration_value = True)
+
+    delaunay_tetra = []
+    for sk in st_delaunay.get_skeleton(4):
+        if len(sk[0]) == 4:
+            tetra = [delaunay.get_point(sk[0][0]),
+                     delaunay.get_point(sk[0][1]),
+                     delaunay.get_point(sk[0][2]),
+                     delaunay.get_point(sk[0][3]) ]
+            delaunay_tetra.append(sorted(tetra, key=lambda tup: tup[0]))
+
+    alpha_tetra = []
+    for sk in st_alpha.get_skeleton(4):
+        if len(sk[0]) == 4:
+            tetra = [alpha.get_point(sk[0][0]),
+                     alpha.get_point(sk[0][1]),
+                     alpha.get_point(sk[0][2]),
+                     alpha.get_point(sk[0][3]) ]
+            alpha_tetra.append(sorted(tetra, key=lambda tup: tup[0]))
+
+    # Check the tetrahedrons from one list are in the second one
+    assert len(alpha_tetra) == len(delaunay_tetra)
+    for tetra_from_del in delaunay_tetra:
+        assert tetra_from_del in alpha_tetra
+
+def test_3d_tetrahedrons():
+    for precision in ['fast', 'safe', 'exact']:
+        _3d_tetrahedrons(precision)
diff --git a/src/python/test/test_tomato.py b/src/python/test/test_tomato.py
new file mode 100755
index 00000000..ecab03c4
--- /dev/null
+++ b/src/python/test/test_tomato.py
@@ -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):       Marc Glisse
+
+    Copyright (C) 2020 Inria
+
+    Modification(s):
+      - YYYY/MM Author: Description of the modification
+"""
+
+from gudhi.clustering.tomato import Tomato
+import numpy as np
+import pytest
+import matplotlib.pyplot as plt
+
+# Disable graphics for testing purposes
+plt.show = lambda: None
+
+
+def test_tomato_1():
+    a = [(1, 2), (1.1, 1.9), (0.9, 1.8), (10, 0), (10.1, 0.05), (10.2, -0.1), (5.4, 0)]
+    t = Tomato(metric="euclidean", n_clusters=2, k=4, n_jobs=-1, eps=0.05)
+    assert np.array_equal(t.fit_predict(a), [1, 1, 1, 0, 0, 0, 0])  # or with swapped 0 and 1
+    assert np.array_equal(t.children_, [[0, 1]])
+
+    t = Tomato(density_type="KDE", r=1, k=4)
+    t.fit(a)
+    assert np.array_equal(t.leaf_labels_, [1, 1, 1, 0, 0, 0, 0])  # or with swapped 0 and 1
+    assert t.n_clusters_ == 2
+    t.merge_threshold_ = 10
+    assert t.n_clusters_ == 1
+    assert (t.labels_ == 0).all()
+
+    t = Tomato(graph_type="radius", r=0.1, metric="cosine", k=3)
+    assert np.array_equal(t.fit_predict(a), [1, 1, 1, 0, 0, 0, 0])  # or with swapped 0 and 1
+
+    t = Tomato(metric="euclidean", graph_type="radius", r=4.7, k=4)
+    t.fit(a)
+    assert t.max_weight_per_cc_.size == 2
+    assert np.array_equal(t.neighbors_, [[0, 1, 2], [0, 1, 2], [0, 1, 2], [3, 4, 5, 6], [3, 4, 5], [3, 4, 5], [3, 6]])
+    t.plot_diagram()
+
+    t = Tomato(graph_type="radius", r=4.7, k=4, symmetrize_graph=True)
+    t.fit(a)
+    assert t.max_weight_per_cc_.size == 2
+    assert [set(i) for i in t.neighbors_] == [{1, 2}, {0, 2}, {0, 1}, {4, 5, 6}, {3, 5}, {3, 4}, {3}]
+
+    t = Tomato(n_clusters=2, k=4, symmetrize_graph=True)
+    t.fit(a)
+    assert [set(i) for i in t.neighbors_] == [
+        {1, 2, 6},
+        {0, 2, 6},
+        {0, 1, 6},
+        {4, 5, 6},
+        {3, 5, 6},
+        {3, 4, 6},
+        {0, 1, 2, 3, 4, 5},
+    ]
+    t.plot_diagram()
+
+    t = Tomato(k=6, metric="manhattan")
+    t.fit(a)
+    assert t.diagram_.size == 0
+    assert t.max_weight_per_cc_.size == 1
+    t.plot_diagram()