Merge master and resolve conflicts

26 files changed, 582 insertions, 188 deletions

diff --git a/.github/for_maintainers/new_gudhi_version_creation.md b/.github/for_maintainers/new_gudhi_version_creation.md
index 86c393a0..4de81b8a 100644
--- a/.github/for_maintainers/new_gudhi_version_creation.md
+++ b/.github/for_maintainers/new_gudhi_version_creation.md
@@ -18,7 +18,7 @@ Checkin the modifications, build and test the version:
 ```bash
 git submodule update --init
 rm -rf build; mkdir build; cd build
-cmake -DCGAL_DIR=/your/path/to/CGAL -DWITH_GUDHI_EXAMPLE=ON -DWITH_GUDHI_BENCHMARK=ON  -DUSER_VERSION_DIR=gudhi.@GUDHI_VERSION@ -DPython_ADDITIONAL_VERSIONS=3 ..
+cmake -DCMAKE_BUILD_TYPE=Release -DCGAL_DIR=/your/path/to/CGAL -DWITH_GUDHI_EXAMPLE=ON -DWITH_GUDHI_BENCHMARK=ON  -DUSER_VERSION_DIR=gudhi.@GUDHI_VERSION@ -DPython_ADDITIONAL_VERSIONS=3 ..
 make user_version
 date +"%d-%m-%Y-%T" > gudhi.@GUDHI_VERSION@/timestamp.txt
 tar -czvf gudhi.@GUDHI_VERSION@.tar.gz gudhi.@GUDHI_VERSION@
@@ -43,8 +43,8 @@ make doxygen  2>&1 | tee dox.log && grep warning dox.log
 cp -R gudhi.@GUDHI_VERSION@/doc/html gudhi.doc.@GUDHI_VERSION@/cpp
 cd gudhi.@GUDHI_VERSION@
 rm -rf build; mkdir build; cd build
-cmake -DCGAL_DIR=/your/path/to/CGAL -DWITH_GUDHI_EXAMPLE=ON -DPython_ADDITIONAL_VERSIONS=3 ..
-export LC_ALL=en_US.UTF-8  # cf. bug
+cmake -DCMAKE_BUILD_TYPE=Release -DCGAL_DIR=/your/path/to/CGAL -DWITH_GUDHI_EXAMPLE=ON -DPython_ADDITIONAL_VERSIONS=3 ..
+export LC_ALL=en_US.UTF-8  # cf. bug https://github.com/GUDHI/gudhi-devel/issues/111
 make sphinx
 ```
 
@@ -82,14 +82,53 @@ ln -s @GUDHI_VERSION@ latest
 
 * Go on page https://github.com/GUDHI/gudhi-devel/releases/new
 * Name the tag: tags/gudhi-release-@GUDHI_VERSION@
-* Name the release GUDHI @GUDHI_VERSION@
+* Name the release GUDHI @GUDHI_VERSION@ release
 * Write the release note
 * Drag'n drop *gudhi.@GUDHI_VERSION@.tar.gz*, *md5sum.txt*, *sha256sum.txt*, *sha512sum.txt* files
 * Tick the *This is a pre-release* check button if this is a release candidate (untick if this is an official version)
 * Click the *Publish the release* button
 
+## Pip package
+
+The pip package construction shall be started on release creation, you just have to check [gudhi github actions](https://github.com/GUDHI/gudhi-devel/actions) results.
+The version number must be conform to [pep440](https://www.python.org/dev/peps/pep-0440/#pre-releases)
+
+## Conda package
+
+You have to fork [conda-forge/gudhi-feedstock](https://github.com/conda-forge/gudhi-feedstock).
+The main changes consist into changing in the `recipe/meta.yaml`:
+* `{% set version = "@GUDHI_VERSION@" %}`
+* The cgal-cpp version number with the last one (you can find it [here](https://anaconda.org/conda-forge/cgal-cpp)) in the `host:` and the `run:` sections
+
+Create a Pull Request (PR) from this fork.
+If you need to update conda tools (conda-build, conda-smithy, ...), add a comment in your PR saying `@conda-forge-admin, please rerender`, it will done automatically (do not forget to `git pull` the changes).
+
+## Docker image
+
+You have to modify the `Dockerfile_gudhi_installation` at the root of this repository in order to use the last release, cf. lines:
+```
+...
+RUN curl -LO "https://github.com/GUDHI/gudhi-devel/releases/download/tags%2Fgudhi-release-@GUDHI_VERSION@/gudhi.@GUDHI_VERSION@.tar.gz" \
+&& tar xf gudhi.@GUDHI_VERSION@.tar.gz \
+&& cd gudhi.@GUDHI_VERSION@ \
+...
+```
+
+Build and push images to docker hub:
+```
+docker build -f Dockerfile_gudhi_installation -t gudhi/latest_gudhi_version:@GUDHI_VERSION@ .
+docker run --rm -it gudhi/latest_gudhi_version:@GUDHI_VERSION@ 
+```
+
+***[Check there are no error with utils and python version]***
+
+```
+docker tag gudhi/latest_gudhi_version:@GUDHI_VERSION@ gudhi/latest_gudhi_version:latest
+docker push gudhi/latest_gudhi_version:latest
+docker push gudhi/latest_gudhi_version:@GUDHI_VERSION@
+```
+
 ## Mail sending
 Send version mail to the following lists :
 * gudhi-devel@lists.gforge.inria.fr
 * gudhi-users@lists.gforge.inria.fr (not for release candidate)
-
diff --git a/.github/next_release.md b/.github/next_release.md
index e73f7c96..cd2376eb 100644
--- a/.github/next_release.md
+++ b/.github/next_release.md
@@ -1,42 +1,19 @@
-We are pleased to announce the release 3.3.0 of the GUDHI library.
+We are pleased to announce the release 3.4.0 of the GUDHI library.
 
-As a major new feature, the GUDHI library now offers a persistence-based clustering algorithm, weighted Rips complex using DTM
-and edge collapse.
+As a major new feature, the GUDHI library now offers ...
 
-The GUDHI library is hosted on GitHub, do not hesitate to [fork the GUDHI project on GitHub](https://github.com/GUDHI/gudhi-devel).
-From a user point of view, we recommend to download GUDHI user version (gudhi.3.3.0.tar.gz).
+We are now using GitHub to develop the GUDHI library, do not hesitate to [fork the GUDHI project on GitHub](https://github.com/GUDHI/gudhi-devel). From a user point of view, we recommend to download GUDHI user version (gudhi.3.4.0.tar.gz).
 
-Below is a list of changes made since GUDHI 3.2.0:
+Below is a list of changes made since GUDHI 3.3.0:
 
-- [DTM density estimator](https://gudhi.inria.fr/python/latest/point_cloud.html#module-gudhi.point_cloud.dtm)
-     - Python implementation of a density estimator based on the distance to the empirical measure defined by a point set.
+- [Module](link)
+     - ...
 
-- [DTM Rips complex](https://gudhi.inria.fr/python/latest/rips_complex_user.html#dtm-rips-complex)
-     - This Python implementation constructs a weighted Rips complex giving larger weights to outliers,
-     which reduces their impact on the persistence diagram
-
-- [Alpha complex](https://gudhi.inria.fr/python/latest/alpha_complex_user.html) - Python interface improvements
-     - 'fast' and 'exact' computations
-     - Delaunay complex construction by not setting filtration values
-     - Use the specific 3d alpha complex automatically to make the computations faster
-
-- [Clustering](https://gudhi.inria.fr/python/latest/clustering.html)
-     - Python implementation of [ToMATo](https://doi.org/10.1145/2535927), a persistence-based clustering algorithm
-
-- [Edge Collapse](https://gudhi.inria.fr/doc/latest/group__edge__collapse.html) of a filtered flag complex
-     - This C++ implementation reduces a filtration of Vietoris-Rips complex from its graph to another smaller
-     flag filtration with the same persistence.
-
-- [Bottleneck distance](https://gudhi.inria.fr/python/latest/bottleneck_distance_user.html)
-     - Python interface to [hera](https://github.com/grey-narn/hera)'s bottleneck distance
-
-- Representations - Python interface change
-     - [Wasserstein metrics](https://gudhi.inria.fr/python/latest/representations.html#gudhi.representations.metrics.WassersteinDistance)
-     is now [hera](https://github.com/grey-narn/hera) by default
+- [Module](link)
+     - ...
 
 - Miscellaneous
-     - The [list of bugs that were solved since GUDHI-3.2.0](https://github.com/GUDHI/gudhi-devel/issues?q=label%3A3.3.0+is%3Aclosed)
-     is available on GitHub.
+     - The [list of bugs that were solved since GUDHI-3.3.0](https://github.com/GUDHI/gudhi-devel/issues?q=label%3A3.4.0+is%3Aclosed) is available on GitHub.
 
 All modules are distributed under the terms of the MIT license.
 However, there are still GPL dependencies for many modules. We invite you to check our [license dedicated web page](https://gudhi.inria.fr/licensing/) for further details.
@@ -48,4 +25,3 @@ We provide [bibtex entries](https://gudhi.inria.fr/doc/latest/_citation.html) fo
 Feel free to [contact us](https://gudhi.inria.fr/contact/) in case you have any questions or remarks.
 
 For further information about downloading and installing the library ([C++](https://gudhi.inria.fr/doc/latest/installation.html) or [Python](https://gudhi.inria.fr/python/latest/installation.html)), please visit the [GUDHI web site](https://gudhi.inria.fr/).
-
diff --git a/.github/workflows/pip-packaging-osx.yml b/.github/workflows/pip-packaging-osx.yml
index 85c3c807..c94369ac 100644
--- a/.github/workflows/pip-packaging-osx.yml
+++ b/.github/workflows/pip-packaging-osx.yml
@@ -22,7 +22,8 @@ jobs:
           architecture: x64
       - name: Install dependencies
         run: |
-          brew update && brew install boost eigen gmp mpfr cgal
+          brew update || true
+          brew install boost eigen gmp mpfr cgal || true
           python -m pip install --user -r .github/build-requirements.txt
           python -m pip install --user twine delocate
       - name: Build python wheel
diff --git a/.github/workflows/pip-packaging-windows.yml b/.github/workflows/pip-packaging-windows.yml
index 1cadf6b1..2e45ad71 100644
--- a/.github/workflows/pip-packaging-windows.yml
+++ b/.github/workflows/pip-packaging-windows.yml
@@ -20,17 +20,24 @@ jobs:
         with:
           python-version: ${{ matrix.python-version }}
           architecture: x64
+      - name: Patch
+        run: |
+          (new-object System.Net.WebClient).DownloadFile('https://github.com/microsoft/vcpkg/files/4978792/vcpkg_fixup_pkgconfig.cmake.txt','c:\vcpkg\scripts\cmake\vcpkg_fixup_pkgconfig.cmake')
+          (new-object System.Net.WebClient).DownloadFile('https://github.com/microsoft/vcpkg/files/4978796/vcpkg_acquire_msys.cmake.txt','c:\vcpkg\scripts\cmake\vcpkg_acquire_msys.cmake')
+        shell: powershell
       - name: Install dependencies
         run: |
-          vcpkg install boost-graph:x64-windows boost-serialization:x64-windows boost-date-time:x64-windows boost-system:x64-windows boost-filesystem:x64-windows boost-units:x64-windows boost-thread:x64-windows boost-program-options:x64-windows eigen3:x64-windows mpfr:x64-windows mpir:x64-windows cgal:x64-windows
+          vcpkg update
+          vcpkg upgrade --no-dry-run
+          vcpkg install boost-graph boost-serialization boost-date-time boost-system boost-filesystem boost-units boost-thread boost-program-options eigen3 mpfr mpir cgal --triplet x64-windows
           python -m pip install --user -r .github/build-requirements.txt
           python -m pip install --user twine
+          python -m pip list
       - name: Build python wheel
         run: |
-          python --version
           mkdir build
           cd build
-          cmake -DCMAKE_BUILD_TYPE=Release -DGMP_INCLUDE_DIR="c:/vcpkg/installed/x64-windows/include" -DGMP_LIBRARIES="c:/vcpkg/installed/x64-windows/lib/mpir.lib" -DGMP_LIBRARIES_DIR="c:/vcpkg/installed/x64-windows/lib" -DCMAKE_TOOLCHAIN_FILE=C:/vcpkg/scripts/buildsystems/vcpkg.cmake -DPython_ADDITIONAL_VERSIONS=3 ..
+          cmake -DCMAKE_BUILD_TYPE=Release -DGMP_INCLUDE_DIR="c:/vcpkg/installed/x64-windows/include" -DGMP_LIBRARIES="c:/vcpkg/installed/x64-windows/lib/mpir.lib" -DGMP_LIBRARIES_DIR="c:/vcpkg/installed/x64-windows/lib" -DCMAKE_TOOLCHAIN_FILE=C:/vcpkg/scripts/buildsystems/vcpkg.cmake -DVCPKG_TARGET_TRIPLET=x64-windows -DPython_ADDITIONAL_VERSIONS=3 ..
           cd src/python
           cp c:/vcpkg/installed/x64-windows/bin/mpfr.dll gudhi/
           cp c:/vcpkg/installed/x64-windows/bin/mpir.dll gudhi/
diff --git a/CMakeGUDHIVersion.txt b/CMakeGUDHIVersion.txt
index a78b8adc..5f1eaacf 100644
--- a/CMakeGUDHIVersion.txt
+++ b/CMakeGUDHIVersion.txt
@@ -1,8 +1,8 @@
 # Must be conform to pep440 - https://www.python.org/dev/peps/pep-0440/#pre-releases
 set (GUDHI_MAJOR_VERSION 3)
-set (GUDHI_MINOR_VERSION 3)
+set (GUDHI_MINOR_VERSION 4)
 # GUDHI_PATCH_VERSION can be 'ZaN' for Alpha release, 'ZbN' for Beta release, 'ZrcN' for release candidate or 'Z' for a final release.
-set (GUDHI_PATCH_VERSION 0rc1)
+set (GUDHI_PATCH_VERSION 0a0)
 set(GUDHI_VERSION ${GUDHI_MAJOR_VERSION}.${GUDHI_MINOR_VERSION}.${GUDHI_PATCH_VERSION})
 
 message(STATUS "GUDHI version : ${GUDHI_VERSION}")
diff --git a/Dockerfile_gudhi_installation b/Dockerfile_gudhi_installation
index 996dd06b..92430fce 100644
--- a/Dockerfile_gudhi_installation
+++ b/Dockerfile_gudhi_installation
@@ -58,9 +58,9 @@ RUN pip3 install \
 # apt clean up
 RUN apt autoremove && rm -rf /var/lib/apt/lists/*
 
-RUN curl -LO "https://github.com/GUDHI/gudhi-devel/releases/download/tags%2Fgudhi-release-3.2.0/gudhi.3.2.0.tar.gz" \
-&& tar xf gudhi.3.2.0.tar.gz \
-&& cd gudhi.3.2.0 \
+RUN curl -LO "https://github.com/GUDHI/gudhi-devel/releases/download/tags%2Fgudhi-release-3.3.0/gudhi.3.3.0.tar.gz" \
+&& tar xf gudhi.3.3.0.tar.gz \
+&& cd gudhi.3.3.0 \
 && mkdir build && cd build && cmake -DCMAKE_BUILD_TYPE=Release -DWITH_GUDHI_PYTHON=OFF -DPython_ADDITIONAL_VERSIONS=3 ..  \
 && make all test install \
 && cmake -DWITH_GUDHI_PYTHON=ON . \
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 29ec23d0..8e88cab5 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -5,11 +5,10 @@ jobs:
     timeoutInMinutes: 0
     cancelTimeoutInMinutes: 60
     pool:
-      vmImage: macOS-10.14
+      vmImage: macOS-10.15
     variables:
       pythonVersion: '3.6'
       cmakeBuildType: Release
-      customInstallation: 'brew update && brew install graphviz doxygen boost eigen gmp mpfr tbb cgal'
 
     steps:
     - bash: echo "##vso[task.prependpath]$CONDA/bin"
@@ -23,7 +22,8 @@ jobs:
         sudo conda install --yes --quiet --name gudhi_build_env python=$(pythonVersion)
         python -m pip install --user -r .github/build-requirements.txt
         python -m pip install --user -r .github/test-requirements.txt
-        $(customInstallation)
+        brew update || true
+        brew install graphviz doxygen boost eigen gmp mpfr tbb cgal || true
       displayName: 'Install build dependencies'
     - bash: |
         source activate gudhi_build_env
diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib
index 9bff14b4..16fa29d0 100644
--- a/biblio/bibliography.bib
+++ b/biblio/bibliography.bib
@@ -576,6 +576,15 @@ note = "http://gmplib.org/",
 
 %TEMPORARY
 %------------------------------------------------------------------
+@misc{royer2019atol,
+    title={ATOL: Measure Vectorisation for Automatic Topologically-Oriented Learning},
+    author={Martin Royer and Frédéric Chazal and Clément Levrard and Yuichi Ike and Yuhei Umeda},
+    year={2019},
+    eprint={1909.13472},
+    archivePrefix={arXiv},
+    primaryClass={cs.CG}
+}
+
 @inproceedings{deSilva:2013:GSP:2493132.2462402,
  author = {de Silva, Vin and Nanda, Vidit},
  title = {Geometry in the space of persistence modules},
diff --git a/src/Cech_complex/utilities/cechcomplex.md b/src/Cech_complex/utilities/cechcomplex.md
index f7817dbb..821e4dad 100644
--- a/src/Cech_complex/utilities/cechcomplex.md
+++ b/src/Cech_complex/utilities/cechcomplex.md
@@ -1,3 +1,13 @@
+---
+layout: page
+title: "Čech complex"
+meta_title: "Čech complex"
+teaser: ""
+permalink: /cechcomplex/
+---
+{::comment}
+Leave the lines above as it is required by the web site generator 'Jekyll'
+{:/comment}
 
 
 # Čech complex #
diff --git a/src/common/doc/header.html b/src/common/doc/header.html
index 99ab6bb7..9da20bbc 100644
--- a/src/common/doc/header.html
+++ b/src/common/doc/header.html
@@ -24,64 +24,65 @@ $extrastylesheet
 
 <!-- GUDHI website header BEGIN -->
 <div id="navigation" class="sticky">
-    <nav class="top-bar" role="navigation" data-topbar>
-      <ul class="title-area">
-        <li class="name">
-        <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI library</a></h1>
-      </li>
-         <!-- Remove the class "menu-icon" to get rid of menu icon. Take out "Menu" to just have icon alone -->
-        <li class="toggle-topbar menu-icon"><a href="#"><span>Navigation</span></a></li>
+  <nav class="top-bar" role="navigation" data-topbar>
+    <ul class="title-area">
+      <li class="name">
+      <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI library</a></h1>
+    </li>
+       <!-- Remove the class "menu-icon" to get rid of menu icon. Take out "Menu" to just have icon alone -->
+      <li class="toggle-topbar menu-icon"><a href="#"><span>Nav</span></a></li>
+    </ul>
+    <section class="top-bar-section">
+      <ul class="right">
+              <li class="divider"></li>
+              <li><a  href="/contact/">Contact</a></li>
       </ul>
-      <section class="top-bar-section">
-        <ul class="right">
-                <li class="divider"></li>
-                <li><a href="/contact/">Contact</a></li>
-        </ul>
-        <ul class="left">
-                <li><a href="/"> <img src="/assets/img/home.png" alt="&nbsp;&nbsp;GUDHI">&nbsp;&nbsp;GUDHI </a></li>
-                <li class="divider"></li>
-                <li class="has-dropdown">
-                  <a href="#">Project</a>
-                    <ul class="dropdown">
-                        <li><a href="/people/">People</a></li>
-                        <li><a href="/keepintouch/">Keep in touch</a></li>
-                        <li><a href="/partners/">Partners and Funding</a></li>
-                        <li><a href="/relatedprojects/">Related projects</a></li>
-                        <li><a href="/theyaretalkingaboutus/">They are talking about us</a></li>
-                        <li><a href="/inaction/">GUDHI in action</a></li>
-                    </ul>
-                </li>
-                <li class="divider"></li>
-                <li class="has-dropdown">
-                  <a href="#">Download</a>
-                    <ul class="dropdown">
-                        <li><a href="/licensing/">Licensing</a></li>
-                        <li><a href="https://github.com/GUDHI/gudhi-devel/releases/latest" target="_blank">Get the latest sources</a></li>
-                        <li><a href="/conda/">Conda package</a></li>
-                        <li><a href="/dockerfile/">Dockerfile</a></li>
-                    </ul>
-                </li>
-                <li class="divider"></li>
-                <li class="has-dropdown">
-                  <a href="#">Documentation</a>
-                    <ul class="dropdown">
-                        <li><a href="/introduction/">Introduction</a></li>
-                        <li><a href="https://gudhi.inria.fr/doc/latest/installation.html">C++ installation manual</a></li>
-                        <li><a href="https://gudhi.inria.fr/doc/latest/">C++ documentation</a></li>
-                        <li><a href="https://gudhi.inria.fr/python/latest/installation.html">Python installation manual</a></li>
-                        <li><a href="https://gudhi.inria.fr/python/latest/">Python documentation</a></li>
-                        <li><a href="/utils/">Utilities</a></li>
-                        <li><a href="/tutorials/">Tutorials</a></li>
-                    </ul>
-                </li>
-                <li class="divider"></li>
-                <li><a href="/interfaces/">Interfaces</a></li>
-                <li class="divider"></li>
-        </ul>
-      </section>
-    </nav>
-  </div><!-- /#navigation -->
-  <!-- GUDHI website header BEGIN -->
+      <ul class="left">
+              <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>
+                  <ul class="dropdown">
+                      <li><a  href="/people/">People</a></li>
+                      <li><a  href="/keepintouch/">Keep in touch</a></li>
+                      <li><a  href="/partners/">Partners and Funding</a></li>
+                      <li><a  href="/relatedprojects/">Related projects</a></li>
+                      <li><a  href="/theyaretalkingaboutus/">They are talking about us</a></li>
+                      <li><a  href="/inaction/">GUDHI in action</a></li>
+                  </ul>
+              </li>
+              <li class="divider"></li>
+              <li class="has-dropdown">
+                <a  href="#">Download</a>
+                  <ul class="dropdown">
+                      <li><a  href="/licensing/">Licensing</a></li>
+                      <li><a  href="https://github.com/GUDHI/gudhi-devel/releases/latest" target="_blank">Get the latest sources</a></li>
+                      <li><a  href="/conda/">Conda package</a></li>
+                      <li><a  href="https://pypi.org/project/gudhi/" target="_blank">Pip package</a></li>
+                      <li><a  href="/dockerfile/">Dockerfile</a></li>
+                  </ul>
+              </li>
+              <li class="divider"></li>
+              <li class="has-dropdown">
+                <a  href="#">Documentation</a>
+                  <ul class="dropdown">
+                      <li><a  href="/introduction/">Introduction</a></li>
+                      <li><a  href="/doc/latest/installation.html">C++ installation manual</a></li>
+                      <li><a  href="/doc/latest/">C++ documentation</a></li>
+                      <li><a  href="/python/latest/installation.html">Python installation manual</a></li>
+                      <li><a  href="/python/latest/">Python documentation</a></li>
+                      <li><a  href="/utils/">Utilities</a></li>
+                      <li><a  href="/tutorials/">Tutorials</a></li>
+                  </ul>
+              </li>
+              <li class="divider"></li>
+              <li><a  href="/interfaces/">Interfaces</a></li>
+              <li class="divider"></li>
+      </ul>
+    </section>
+  </nav>
+</div><!-- /#navigation -->
+<!-- GUDHI website header END -->
 
 <div id="top"><!-- do not remove this div, it is closed by doxygen! -->
 
diff --git a/src/python/doc/_templates/layout.html b/src/python/doc/_templates/layout.html
index a672a281..cd40a51b 100644
--- a/src/python/doc/_templates/layout.html
+++ b/src/python/doc/_templates/layout.html
@@ -175,58 +175,59 @@
         <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI library</a></h1>
       </li>
          <!-- Remove the class "menu-icon" to get rid of menu icon. Take out "Menu" to just have icon alone -->
-        <li class="toggle-topbar menu-icon"><a href="#"><span>Navigation</span></a></li>
+        <li class="toggle-topbar menu-icon"><a href="#"><span>Nav</span></a></li>
       </ul>
       <section class="top-bar-section">
         <ul class="right">
                 <li class="divider"></li>
-                <li><a href="/contact/">Contact</a></li>
+                <li><a  href="/contact/">Contact</a></li>
         </ul>
         <ul class="left">
-                <li><a href="/"> <img src="/assets/img/home.png" alt="&nbsp;&nbsp;GUDHI">&nbsp;&nbsp;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>
+                  <a  href="#">Project</a>
                     <ul class="dropdown">
-                        <li><a href="/people/">People</a></li>
-                        <li><a href="/keepintouch/">Keep in touch</a></li>
-                        <li><a href="/partners/">Partners and Funding</a></li>
-                        <li><a href="/relatedprojects/">Related projects</a></li>
-                        <li><a href="/theyaretalkingaboutus/">They are talking about us</a></li>
-                        <li><a href="/inaction/">GUDHI in action</a></li>
+                        <li><a  href="/people/">People</a></li>
+                        <li><a  href="/keepintouch/">Keep in touch</a></li>
+                        <li><a  href="/partners/">Partners and Funding</a></li>
+                        <li><a  href="/relatedprojects/">Related projects</a></li>
+                        <li><a  href="/theyaretalkingaboutus/">They are talking about us</a></li>
+                        <li><a  href="/inaction/">GUDHI in action</a></li>
                     </ul>
                 </li>
                 <li class="divider"></li>
                 <li class="has-dropdown">
-                  <a href="#">Download</a>
+                  <a  href="#">Download</a>
                     <ul class="dropdown">
-                        <li><a href="/licensing/">Licensing</a></li>
-                        <li><a href="https://github.com/GUDHI/gudhi-devel/releases/latest" target="_blank">Get the latest sources</a></li>
-                        <li><a href="/conda/">Conda package</a></li>
-                        <li><a href="/dockerfile/">Dockerfile</a></li>
+                        <li><a  href="/licensing/">Licensing</a></li>
+                        <li><a  href="https://github.com/GUDHI/gudhi-devel/releases/latest" target="_blank">Get the latest sources</a></li>
+                        <li><a  href="/conda/">Conda package</a></li>
+                        <li><a  href="https://pypi.org/project/gudhi/" target="_blank">Pip package</a></li>
+                        <li><a  href="/dockerfile/">Dockerfile</a></li>
                     </ul>
                 </li>
                 <li class="divider"></li>
                 <li class="has-dropdown">
-                  <a href="#">Documentation</a>
+                  <a  href="#">Documentation</a>
                     <ul class="dropdown">
-                        <li><a href="/introduction/">Introduction</a></li>
-                        <li><a href="https://gudhi.inria.fr/doc/latest/installation.html">C++ installation manual</a></li>
-                        <li><a href="https://gudhi.inria.fr/doc/latest/">C++ documentation</a></li>
-                        <li><a href="https://gudhi.inria.fr/python/latest/installation.html">Python installation manual</a></li>
-                        <li><a href="https://gudhi.inria.fr/python/latest/">Python documentation</a></li>
-                        <li><a href="/utils/">Utilities</a></li>
-                        <li><a href="/tutorials/">Tutorials</a></li>
+                        <li><a  href="/introduction/">Introduction</a></li>
+                        <li><a  href="/doc/latest/installation.html">C++ installation manual</a></li>
+                        <li><a  href="/doc/latest/">C++ documentation</a></li>
+                        <li><a  href="/python/latest/installation.html">Python installation manual</a></li>
+                        <li><a  href="/python/latest/">Python documentation</a></li>
+                        <li><a  href="/utils/">Utilities</a></li>
+                        <li><a  href="/tutorials/">Tutorials</a></li>
                     </ul>
                 </li>
                 <li class="divider"></li>
-                <li><a href="/interfaces/">Interfaces</a></li>
+                <li><a  href="/interfaces/">Interfaces</a></li>
                 <li class="divider"></li>
         </ul>
       </section>
     </nav>
-  </div><!-- /#navigation -->  
-  <!-- GUDHI website header BEGIN -->
+  </div><!-- /#navigation -->
+  <!-- GUDHI website header END -->
 
 
 {%- block header %}{% endblock %}
diff --git a/src/python/doc/examples.rst b/src/python/doc/examples.rst
index a42227e3..76e5d4c7 100644
--- a/src/python/doc/examples.rst
+++ b/src/python/doc/examples.rst
@@ -7,27 +7,30 @@ Examples
 
 .. only:: builder_html
 
-    * :download:`rips_complex_from_points_example.py <../example/rips_complex_from_points_example.py>`
+    * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>`
     * :download:`alpha_complex_from_points_example.py <../example/alpha_complex_from_points_example.py>`
-    * :download:`simplex_tree_example.py <../example/simplex_tree_example.py>`
     * :download:`alpha_rips_persistence_bottleneck_distance.py <../example/alpha_rips_persistence_bottleneck_distance.py>`
-    * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>`
-    * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>`
-    * :download:`periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py <../example/periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py>`
     * :download:`bottleneck_basic_example.py <../example/bottleneck_basic_example.py>`
-    * :download:`gudhi_graphical_tools_example.py <../example/gudhi_graphical_tools_example.py>`
-    * :download:`plot_simplex_tree_dim012.py <../example/plot_simplex_tree_dim012.py>`
-    * :download:`plot_rips_complex.py <../example/plot_rips_complex.py>`
-    * :download:`plot_alpha_complex.py <../example/plot_alpha_complex.py>`
-    * :download:`witness_complex_from_nearest_landmark_table.py <../example/witness_complex_from_nearest_landmark_table.py>`
+    * :download:`coordinate_graph_induced_complex.py <../example/coordinate_graph_induced_complex.py>`
+    * :download:`diagram_vectorizations_distances_kernels.py <../example/diagram_vectorizations_distances_kernels.py>`
     * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>`
     * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>`
-    * :download:`rips_complex_diagram_persistence_from_off_file_example.py <../example/rips_complex_diagram_persistence_from_off_file_example.py>`
+    * :download:`functional_graph_induced_complex.py <../example/functional_graph_induced_complex.py>`
+    * :download:`gudhi_graphical_tools_example.py <../example/gudhi_graphical_tools_example.py>`
+    * :download:`nerve_of_a_covering.py <../example/nerve_of_a_covering.py>`
+    * :download:`periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py <../example/periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py>`
+    * :download:`plot_alpha_complex.py <../example/plot_alpha_complex.py>`
+    * :download:`plot_rips_complex.py <../example/plot_rips_complex.py>`
+    * :download:`plot_simplex_tree_dim012.py <../example/plot_simplex_tree_dim012.py>`
+    * :download:`random_cubical_complex_persistence_example.py <../example/random_cubical_complex_persistence_example.py>`
+    * :download:`rips_complex_diagram_persistence_from_correlation_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_correlation_matrix_file_example.py>`
     * :download:`rips_complex_diagram_persistence_from_distance_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_distance_matrix_file_example.py>`
+    * :download:`rips_complex_diagram_persistence_from_off_file_example.py <../example/rips_complex_diagram_persistence_from_off_file_example.py>`
+    * :download:`rips_complex_edge_collapse_example.py <../example/rips_complex_edge_collapse_example.py>`
+    * :download:`rips_complex_from_points_example.py <../example/rips_complex_from_points_example.py>`
     * :download:`rips_persistence_diagram.py <../example/rips_persistence_diagram.py>`
+    * :download:`simplex_tree_example.py <../example/simplex_tree_example.py>`
     * :download:`sparse_rips_persistence_diagram.py <../example/sparse_rips_persistence_diagram.py>`
-    * :download:`random_cubical_complex_persistence_example.py <../example/random_cubical_complex_persistence_example.py>`
-    * :download:`coordinate_graph_induced_complex.py <../example/coordinate_graph_induced_complex.py>`
-    * :download:`functional_graph_induced_complex.py <../example/functional_graph_induced_complex.py>`
+    * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>`
     * :download:`voronoi_graph_induced_complex.py <../example/voronoi_graph_induced_complex.py>`
-    * :download:`nerve_of_a_covering.py <../example/nerve_of_a_covering.py>`
+    * :download:`witness_complex_from_nearest_landmark_table.py <../example/witness_complex_from_nearest_landmark_table.py>`
diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst
index 525ca84e..78e1af73 100644
--- a/src/python/doc/installation.rst
+++ b/src/python/doc/installation.rst
@@ -323,6 +323,35 @@ The following examples require the `Matplotlib <http://matplotlib.org>`_:
     * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>`
     * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>`
 
+LaTeX
+~~~~~
+
+If a sufficiently complete LaTeX toolchain is available (including dvipng and ghostscript), the LaTeX option of
+matplotlib is enabled for prettier captions (cf.
+`matplotlib text rendering with LaTeX <https://matplotlib.org/3.3.0/tutorials/text/usetex.html>`_).
+It also requires `type1cm` LaTeX package (not detected by matplotlib).
+
+If you are facing issues with LaTeX rendering, like this one:
+
+.. code-block:: none
+
+    Traceback (most recent call last):
+      File "/usr/lib/python3/dist-packages/matplotlib/texmanager.py", line 302, in _run_checked_subprocess
+        report = subprocess.check_output(command,
+    ...
+    ! LaTeX Error: File `type1cm.sty' not found.
+    ...
+
+This is because the LaTeX package is not installed on your system. On Ubuntu systems you can install texlive-full
+(for all LaTeX packages), or more specific packages like texlive-latex-extra, cm-super.
+
+You can still deactivate LaTeX rendering by saying:
+
+.. code-block:: python
+
+    import gudhi
+    gudhi.persistence_graphical_tools._gudhi_matplotlib_use_tex=False
+
 PyKeOps
 -------
 
diff --git a/src/python/doc/persistence_graphical_tools_user.rst b/src/python/doc/persistence_graphical_tools_user.rst
index b5a38eb1..d95b9d2b 100644
--- a/src/python/doc/persistence_graphical_tools_user.rst
+++ b/src/python/doc/persistence_graphical_tools_user.rst
@@ -90,3 +90,14 @@ If you want more information on a specific dimension, for instance:
     gudhi.plot_persistence_density(persistence=pers_diag,
         dimension=1, legend=True, axes=axes[1])
     plt.show()
+
+LaTeX support
+-------------
+
+If you are facing issues with `LaTeX <installation.html#latex>`_ rendering, you can still deactivate LaTeX rendering by
+saying:
+
+.. code-block:: python
+
+    import gudhi
+    gudhi.persistence_graphical_tools._gudhi_matplotlib_use_tex=False
diff --git a/src/python/doc/representations_sum.inc b/src/python/doc/representations_sum.inc
index 323a0920..4298aea9 100644
--- a/src/python/doc/representations_sum.inc
+++ b/src/python/doc/representations_sum.inc
@@ -2,7 +2,7 @@
    :widths: 30 40 30
 
    +------------------------------------------------------------------+----------------------------------------------------------------+-------------------------------------------------------------+
-   | .. figure::                                                      | Vectorizations, distances and kernels that work on persistence | :Author: Mathieu Carrière                                   |
+   | .. figure::                                                      | Vectorizations, distances and kernels that work on persistence | :Author: Mathieu Carrière, Martin Royer                     |
    |      img/sklearn-tda.png                                         | diagrams, compatible with scikit-learn.                        |                                                             |
    |                                                                  |                                                                | :Since: GUDHI 3.1.0                                         |
    |                                                                  |                                                                |                                                             |
diff --git a/src/python/example/rips_complex_edge_collapse_example.py b/src/python/example/rips_complex_edge_collapse_example.py
new file mode 100755
index 00000000..b26eb9fc
--- /dev/null
+++ b/src/python/example/rips_complex_edge_collapse_example.py
@@ -0,0 +1,62 @@
+#!/usr/bin/env python
+
+import gudhi
+import matplotlib.pyplot as plt
+import time
+
+""" 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) 2016 Inria
+
+    Modification(s):
+      - YYYY/MM Author: Description of the modification
+"""
+
+__author__ = "Vincent Rouvreau"
+__copyright__ = "Copyright (C) 2020 Inria"
+__license__ = "MIT"
+
+
+print("#####################################################################")
+print("RipsComplex (only the one-skeleton) creation from tore3D_300.off file")
+
+off_file = gudhi.__root_source_dir__ + '/data/points/tore3D_300.off'
+point_cloud = gudhi.read_points_from_off_file(off_file = off_file)
+rips_complex = gudhi.RipsComplex(points=point_cloud, max_edge_length=12.0)
+simplex_tree = rips_complex.create_simplex_tree(max_dimension=1)
+print('1. Rips complex is of dimension ', simplex_tree.dimension(), ' - ',
+      simplex_tree.num_simplices(), ' simplices - ',
+      simplex_tree.num_vertices(), ' vertices.')
+
+# Expansion of this one-skeleton would require a lot of memory. Let's collapse it
+start = time.process_time()
+simplex_tree.collapse_edges()
+print('2. Rips complex is of dimension ', simplex_tree.dimension(), ' - ',
+      simplex_tree.num_simplices(), ' simplices - ',
+      simplex_tree.num_vertices(), ' vertices.')
+simplex_tree.expansion(3)
+diag = simplex_tree.persistence()
+print("Collapse, expansion and persistence computation took ", time.process_time() - start, " sec.")
+
+# Use subplots to display diagram and density side by side
+fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(12, 5))
+gudhi.plot_persistence_diagram(diag, axes=axes[0])
+axes[0].set_title("Persistence after 1 collapse")
+
+# Collapse can be performed several times. Let's collapse it 3 times
+start = time.process_time()
+simplex_tree.collapse_edges(nb_iterations = 3)
+print('3. Rips complex is of dimension ', simplex_tree.dimension(), ' - ',
+      simplex_tree.num_simplices(), ' simplices - ',
+      simplex_tree.num_vertices(), ' vertices.')
+simplex_tree.expansion(3)
+diag = simplex_tree.persistence()
+print("Collapse, expansion and persistence computation took ", time.process_time() - start, " sec.")
+
+gudhi.plot_persistence_diagram(diag, axes=axes[1])
+axes[1].set_title("Persistence after 3 more collapses")
+
+# Plot the 2 persistence diagrams side to side to check the persistence is the same
+plt.show()
\ No newline at end of file
diff --git a/src/python/gudhi/persistence_graphical_tools.py b/src/python/gudhi/persistence_graphical_tools.py
index c6766c70..848dc03e 100644
--- a/src/python/gudhi/persistence_graphical_tools.py
+++ b/src/python/gudhi/persistence_graphical_tools.py
@@ -20,6 +20,7 @@ __author__ = "Vincent Rouvreau, Bertrand Michel, Theo Lacombe"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
 
+_gudhi_matplotlib_use_tex = True
 
 def __min_birth_max_death(persistence, band=0.0):
     """This function returns (min_birth, max_death) from the persistence.
@@ -117,10 +118,13 @@ def plot_persistence_barcode(
     try:
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
-        if _matplotlib_can_use_tex():
-            from matplotlib import rc
+        from matplotlib import rc
+        if _gudhi_matplotlib_use_tex and _matplotlib_can_use_tex():
             plt.rc('text', usetex=True)
             plt.rc('font', family='serif')
+        else:
+            plt.rc('text', usetex=False)
+            plt.rc('font', family='DejaVu Sans')
 
         if persistence_file != "":
             if path.isfile(persistence_file):
@@ -263,10 +267,13 @@ def plot_persistence_diagram(
     try:
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
-        if _matplotlib_can_use_tex():
-            from matplotlib import rc
+        from matplotlib import rc
+        if _gudhi_matplotlib_use_tex and _matplotlib_can_use_tex():
             plt.rc('text', usetex=True)
             plt.rc('font', family='serif')
+        else:
+            plt.rc('text', usetex=False)
+            plt.rc('font', family='DejaVu Sans')
 
         if persistence_file != "":
             if path.isfile(persistence_file):
@@ -436,10 +443,13 @@ def plot_persistence_density(
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
         from scipy.stats import kde
-        if _matplotlib_can_use_tex():
-            from matplotlib import rc
+        from matplotlib import rc
+        if _gudhi_matplotlib_use_tex and _matplotlib_can_use_tex():
             plt.rc('text', usetex=True)
             plt.rc('font', family='serif')
+        else:
+            plt.rc('text', usetex=False)
+            plt.rc('font', family='DejaVu Sans')
 
         if persistence_file != "":
             if dimension is None:
diff --git a/src/python/gudhi/point_cloud/knn.py b/src/python/gudhi/point_cloud/knn.py
index 4652fe80..994be3b6 100644
--- a/src/python/gudhi/point_cloud/knn.py
+++ b/src/python/gudhi/point_cloud/knn.py
@@ -46,7 +46,7 @@ class KNearestNeighbors:
             sort_results (bool): if True, then distances and indices of each point are
                 sorted on return, so that the first column contains the closest points.
                 Otherwise, neighbors are returned in an arbitrary order. Defaults to True.
-            enable_autodiff (bool): if the input is a torch.tensor, jax.numpy.ndarray or tensorflow.Tensor, this
+            enable_autodiff (bool): if the input is a torch.tensor or tensorflow.Tensor, this
                 instructs the function to compute distances in a way that works with automatic differentiation.
                 This is experimental, not supported for all metrics, and requires the package EagerPy.
                 Defaults to False.
diff --git a/src/python/gudhi/representations/vector_methods.py b/src/python/gudhi/representations/vector_methods.py
index 46fee086..5ca127f6 100644
--- a/src/python/gudhi/representations/vector_methods.py
+++ b/src/python/gudhi/representations/vector_methods.py
@@ -1,16 +1,17 @@
 # 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):       Mathieu Carrière
+# Author(s):       Mathieu Carrière, Martin Royer
 #
-# Copyright (C) 2018-2019 Inria
+# Copyright (C) 2018-2020 Inria
 #
 # Modification(s):
-#   - YYYY/MM Author: Description of the modification
+#   - 2020/06 Martin: ATOL integration
 
 import numpy as np
 from sklearn.base          import BaseEstimator, TransformerMixin
 from sklearn.preprocessing import MinMaxScaler, MaxAbsScaler
 from sklearn.neighbors     import DistanceMetric
+from sklearn.metrics       import pairwise
 
 from .preprocessing import DiagramScaler, BirthPersistenceTransform
 
@@ -574,3 +575,140 @@ class ComplexPolynomial(BaseEstimator, TransformerMixin):
             numpy array with shape (**threshold**): output complex vector of coefficients.
         """
         return self.fit_transform([diag])[0,:]
+
+def _lapl_contrast(measure, centers, inertias):
+    """contrast function for vectorising `measure` in ATOL"""
+    return np.exp(-pairwise.pairwise_distances(measure, Y=centers) / inertias)
+
+def _gaus_contrast(measure, centers, inertias):
+    """contrast function for vectorising `measure` in ATOL"""
+    return np.exp(-pairwise.pairwise_distances(measure, Y=centers, squared=True) / inertias**2)
+
+def _indicator_contrast(diags, centers, inertias):
+    """contrast function for vectorising `measure` in ATOL"""
+    robe_curve = np.clip(2-pairwise.pairwise_distances(diags, Y=centers)/inertias, 0, 1)
+    return robe_curve
+
+def _cloud_weighting(measure):
+    """automatic uniform weighting with mass 1 for `measure` in ATOL"""
+    return np.ones(shape=measure.shape[0])
+
+def _iidproba_weighting(measure):
+    """automatic uniform weighting with mass 1/N for `measure` in ATOL"""
+    return np.ones(shape=measure.shape[0]) / measure.shape[0]
+
+class Atol(BaseEstimator, TransformerMixin):
+    """
+    This class allows to vectorise measures (e.g. point clouds, persistence diagrams, etc) after a quantisation step.
+
+    ATOL paper: :cite:`royer2019atol`
+
+    Example
+    --------
+    >>> from sklearn.cluster import KMeans
+    >>> from gudhi.representations.vector_methods import Atol
+    >>> import numpy as np
+    >>> a = np.array([[1, 2, 4], [1, 4, 0], [1, 0, 4]])
+    >>> b = np.array([[4, 2, 0], [4, 4, 0], [4, 0, 2]])
+    >>> c = np.array([[3, 2, -1], [1, 2, -1]])
+    >>> atol_vectoriser = Atol(quantiser=KMeans(n_clusters=2, random_state=202006))
+    >>> atol_vectoriser.fit(X=[a, b, c]).centers
+    array([[ 2.        ,  0.66666667,  3.33333333],
+           [ 2.6       ,  2.8       , -0.4       ]])
+    >>> atol_vectoriser(a)
+    array([1.18168665, 0.42375966])
+    >>> atol_vectoriser(c)
+    array([0.02062512, 1.25157463])
+    >>> atol_vectoriser.transform(X=[a, b, c])
+    array([[1.18168665, 0.42375966],
+           [0.29861028, 1.06330156],
+           [0.02062512, 1.25157463]])
+    """
+    def __init__(self, quantiser, weighting_method="cloud", contrast="gaussian"):
+        """
+        Constructor for the Atol measure vectorisation class.
+
+        Parameters:
+            quantiser (Object): Object with `fit` (sklearn API consistent) and `cluster_centers` and `n_clusters`
+                attributes, e.g. sklearn.cluster.KMeans. It will be fitted when the Atol object function `fit` is called.
+            weighting_method (string): constant generic function for weighting the measure points
+                choose from {"cloud", "iidproba"}
+                (default: constant function, i.e. the measure is seen as a point cloud by default).
+                This will have no impact if weights are provided along with measures all the way: `fit` and `transform`.
+            contrast (string): constant function for evaluating proximity of a measure with respect to centers
+                choose from {"gaussian", "laplacian", "indicator"}
+                (default: gaussian contrast function, see page 3 in the ATOL paper).
+        """
+        self.quantiser = quantiser
+        self.contrast = {
+            "gaussian": _gaus_contrast,
+            "laplacian": _lapl_contrast,
+            "indicator": _indicator_contrast,
+        }.get(contrast, _gaus_contrast)
+        self.weighting_method = {
+            "cloud"   : _cloud_weighting,
+            "iidproba": _iidproba_weighting,
+        }.get(weighting_method, _cloud_weighting)
+
+    def fit(self, X, y=None, sample_weight=None):
+        """
+        Calibration step: fit centers to the sample measures and derive inertias between centers.
+
+        Parameters:
+            X (list N x d numpy arrays): input measures in R^d from which to learn center locations and inertias
+                (measures can have different N).
+            y: Ignored, present for API consistency by convention.
+            sample_weight (list of numpy arrays): weights for each measure point in X, optional.
+                If None, the object's weighting_method will be used.
+
+        Returns:
+            self
+        """
+        if not hasattr(self.quantiser, 'fit'):
+            raise TypeError("quantiser %s has no `fit` attribute." % (self.quantiser))
+        if sample_weight is None:
+            sample_weight = np.concatenate([self.weighting_method(measure) for measure in X])
+
+        measures_concat = np.concatenate(X)
+        self.quantiser.fit(X=measures_concat, sample_weight=sample_weight)
+        self.centers = self.quantiser.cluster_centers_
+        if self.quantiser.n_clusters == 1:
+            dist_centers = pairwise.pairwise_distances(measures_concat)
+            np.fill_diagonal(dist_centers, 0)
+            self.inertias = np.array([np.max(dist_centers)/2])
+        else:
+            dist_centers = pairwise.pairwise_distances(self.centers)
+            dist_centers[dist_centers == 0] = np.inf
+            self.inertias = np.min(dist_centers, axis=0)/2
+        return self
+
+    def __call__(self, measure, sample_weight=None):
+        """
+        Apply measure vectorisation on a single measure.
+
+        Parameters:
+            measure (n x d numpy array): input measure in R^d.
+
+        Returns:
+            numpy array in R^self.quantiser.n_clusters.
+        """
+        if sample_weight is None:
+            sample_weight = self.weighting_method(measure)
+        return np.sum(sample_weight * self.contrast(measure, self.centers, self.inertias.T).T, axis=1)
+
+    def transform(self, X, sample_weight=None):
+        """
+        Apply measure vectorisation on a list of measures.
+
+        Parameters:
+            X (list N x d numpy arrays): input measures in R^d from which to learn center locations and inertias
+                (measures can have different N).
+            sample_weight (list of numpy arrays): weights for each measure point in X, optional.
+                If None, the object's weighting_method will be used.
+
+        Returns:
+            numpy array with shape (number of measures) x (self.quantiser.n_clusters).
+        """
+        if sample_weight is None:
+            sample_weight = [self.weighting_method(measure) for measure in X]
+        return np.stack([self(measure, sample_weight=weight) for measure, weight in zip(X, sample_weight)])
diff --git a/src/python/gudhi/simplex_tree.pxd b/src/python/gudhi/simplex_tree.pxd
index 12c2065e..3b494ba3 100644
--- a/src/python/gudhi/simplex_tree.pxd
+++ b/src/python/gudhi/simplex_tree.pxd
@@ -57,6 +57,7 @@ cdef extern from "Simplex_tree_interface.h" namespace "Gudhi":
         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
         void reset_filtration(double filtration, int dimension) nogil
         # Iterators over Simplex tree
         pair[vector[int], double] get_simplex_and_filtration(Simplex_tree_simplex_handle f_simplex) nogil
diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx
index 41b06116..b7682693 100644
--- a/src/python/gudhi/simplex_tree.pyx
+++ b/src/python/gudhi/simplex_tree.pyx
@@ -69,7 +69,7 @@ cdef class SimplexTree:
         this simplicial complex, or +infinity if it is not in the complex.
 
         :param simplex: The N-simplex, represented by a list of vertex.
-        :type simplex: list of int.
+        :type simplex: list of int
         :returns:  The simplicial complex filtration value.
         :rtype:  float
         """
@@ -80,7 +80,7 @@ cdef class SimplexTree:
         given N-simplex.
 
         :param simplex: The N-simplex, represented by a list of vertex.
-        :type simplex: list of int.
+        :type simplex: list of int
         :param filtration:  The new filtration value.
         :type filtration:  float
 
@@ -153,7 +153,7 @@ cdef class SimplexTree:
         """This function sets the dimension of the simplicial complex.
 
         :param dimension: The new dimension value.
-        :type dimension: int.
+        :type dimension: int
 
         .. note::
 
@@ -172,7 +172,7 @@ cdef class SimplexTree:
         complex or not.
 
         :param simplex: The N-simplex to find, represented by a list of vertex.
-        :type simplex: list of int.
+        :type simplex: list of int
         :returns:  true if the simplex was found, false otherwise.
         :rtype:  bool
         """
@@ -186,9 +186,9 @@ cdef class SimplexTree:
 
         :param simplex: The N-simplex to insert, represented by a list of
             vertex.
-        :type simplex: list of int.
+        :type simplex: list of int
         :param filtration: The filtration value of the simplex.
-        :type filtration: float.
+        :type filtration: float
         :returns:  true if the simplex was not yet in the complex, false
             otherwise (whatever its original filtration value).
         :rtype:  bool
@@ -228,7 +228,7 @@ cdef class SimplexTree:
         """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.
+        :type dimension: int
         :returns:  The (simplices of the) skeleton of a maximum dimension.
         :rtype:  generator with tuples(simplex, filtration)
         """
@@ -243,7 +243,7 @@ cdef class SimplexTree:
         """This function returns the star of a given N-simplex.
 
         :param simplex: The N-simplex, represented by a list of vertex.
-        :type simplex: list of int.
+        :type simplex: list of int
         :returns:  The (simplices of the) star of a simplex.
         :rtype:  list of tuples(simplex, filtration)
         """
@@ -265,10 +265,10 @@ cdef class SimplexTree:
         given codimension.
 
         :param simplex: The N-simplex, represented by a list of vertex.
-        :type simplex: list of int.
+        :type simplex: list of int
         :param codimension: The codimension. If codimension = 0, all cofaces
             are returned (equivalent of get_star function)
-        :type codimension: int.
+        :type codimension: int
         :returns:  The (simplices of the) cofaces of a simplex
         :rtype:  list of tuples(simplex, filtration)
         """
@@ -290,7 +290,7 @@ cdef class SimplexTree:
         complex.
 
         :param simplex: The N-simplex, represented by a list of vertex.
-        :type simplex: list of int.
+        :type simplex: list of int
 
         .. note::
 
@@ -308,7 +308,7 @@ cdef class SimplexTree:
         """Prune above filtration value given as parameter.
 
         :param filtration: Maximum threshold value.
-        :type filtration: float.
+        :type filtration: float
         :returns: The filtration modification information.
         :rtype: bool
 
@@ -342,7 +342,7 @@ cdef class SimplexTree:
         1 when calling the method.
 
         :param max_dim: The maximal dimension.
-        :type max_dim: int.
+        :type max_dim: int
         """
         cdef int maxdim = max_dim
         with nogil:
@@ -393,12 +393,12 @@ cdef class SimplexTree:
 
         :param homology_coeff_field: The homology coefficient field. Must be a
             prime number. Default value is 11.
-        :type homology_coeff_field: int.
+        :type homology_coeff_field: int
         :param min_persistence: The minimum persistence value (i.e., the absolute value of the difference between the persistence diagram point coordinates) to take into
             account (strictly greater than min_persistence). Default value is
             0.0.
             Sets min_persistence to -1.0 to see all values.
-        :type min_persistence: float.
+        :type min_persistence: float
         :returns: A list of four persistence diagrams in the format described in :func:`persistence`. The first one is Ordinary, the second one is Relative, the third one is Extended+ and the fourth one is Extended-. See https://link.springer.com/article/10.1007/s10208-008-9027-z and/or section 2.2 in https://link.springer.com/article/10.1007/s10208-017-9370-z for a description of these subtypes.
 
         .. note::
@@ -425,12 +425,12 @@ cdef class SimplexTree:
 
         :param homology_coeff_field: The homology coefficient field. Must be a
             prime number. Default value is 11.
-        :type homology_coeff_field: int.
+        :type homology_coeff_field: int
         :param min_persistence: The minimum persistence value to take into
             account (strictly greater than min_persistence). Default value is
             0.0.
             Set min_persistence to -1.0 to see all values.
-        :type min_persistence: float.
+        :type min_persistence: float
         :param persistence_dim_max: If true, the persistent homology for the
             maximal dimension in the complex is computed. If false, it is
             ignored. Default is false.
@@ -448,12 +448,12 @@ cdef class SimplexTree:
 
         :param homology_coeff_field: The homology coefficient field. Must be a
             prime number. Default value is 11.
-        :type homology_coeff_field: int.
+        :type homology_coeff_field: int
         :param min_persistence: The minimum persistence value to take into
             account (strictly greater than min_persistence). Default value is
             0.0.
             Sets min_persistence to -1.0 to see all values.
-        :type min_persistence: float.
+        :type min_persistence: float
         :param persistence_dim_max: If true, the persistent homology for the
             maximal dimension in the complex is computed. If false, it is
             ignored. Default is false.
@@ -488,10 +488,10 @@ cdef class SimplexTree:
 
         :param from_value: The persistence birth limit to be added in the
             numbers (persistent birth <= from_value).
-        :type from_value: float.
+        :type from_value: float
         :param to_value: The persistence death limit to be added in the
             numbers (persistent death > to_value).
-        :type to_value: float.
+        :type to_value: float
 
         :returns: The persistent Betti numbers ([B0, B1, ..., Bn]).
         :rtype:  list of int
@@ -508,7 +508,7 @@ cdef class SimplexTree:
         complex in a specific dimension.
 
         :param dimension: The specific dimension.
-        :type dimension: int.
+        :type dimension: int
         :returns: The persistence intervals.
         :rtype:  numpy array of dimension 2
 
@@ -537,7 +537,7 @@ cdef class SimplexTree:
         complex in a user given file name.
 
         :param persistence_file: Name of the file.
-        :type persistence_file: string.
+        :type persistence_file: string
 
         :note: intervals_in_dim function requires
             :func:`compute_persistence`
@@ -591,3 +591,23 @@ cdef class SimplexTree:
             infinite0 = np_array(next(l))
             infinites = [np_array(d).reshape(-1,2) for d in l]
         return (normal0, normals, infinite0, infinites)
+
+    def collapse_edges(self, nb_iterations = 1):
+        """Assuming the simplex tree is a 1-skeleton graph, this method collapse edges (simplices of higher dimension
+        are ignored) and resets the simplex tree from the remaining edges.
+        A good candidate is to build a simplex tree on top of a :class:`~gudhi.RipsComplex` of dimension 1 before
+        collapsing edges
+        (cf. :download:`rips_complex_edge_collapse_example.py <../example/rips_complex_edge_collapse_example.py>`).
+        For implementation details, please refer to :cite:`edgecollapsesocg2020`.
+
+        :param nb_iterations: The number of edge collapse iterations to perform. Default is 1.
+        :type nb_iterations: int
+        """
+        # Backup old pointer
+        cdef Simplex_tree_interface_full_featured* ptr = self.get_ptr()
+        cdef int nb_iter = nb_iterations
+        with nogil:
+            # New pointer is a new collapsed simplex tree
+            self.thisptr = <intptr_t>(ptr.collapse_edges(nb_iter))
+            # Delete old pointer
+            del ptr
diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py
index b37d30bb..a9d1cdff 100644
--- a/src/python/gudhi/wasserstein/wasserstein.py
+++ b/src/python/gudhi/wasserstein/wasserstein.py
@@ -99,7 +99,7 @@ def wasserstein_distance(X, Y, matching=False, order=1., internal_p=np.inf, enab
     :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 `np.inf`.
-    :param enable_autodiff: If X and Y are torch.tensor, tensorflow.Tensor or jax.numpy.ndarray, make the computation
+    :param enable_autodiff: If X and Y are torch.tensor or tensorflow.Tensor, make the computation
         transparent to automatic differentiation. This requires the package EagerPy and is currently incompatible
         with `matching=True`.
 
@@ -165,9 +165,9 @@ def wasserstein_distance(X, Y, matching=False, order=1., internal_p=np.inf, enab
         # empty arrays are not handled properly by the helpers, so we avoid calling them
         if len(pairs_X_Y):
             dists.append((Y_orig[pairs_X_Y[:, 1]] - X_orig[pairs_X_Y[:, 0]]).norms.lp(internal_p, axis=-1).norms.lp(order))
-        if len(pairs_X_diag):
+        if len(pairs_X_diag[0]):
             dists.append(_perstot_autodiff(X_orig[pairs_X_diag], order, internal_p))
-        if len(pairs_Y_diag):
+        if len(pairs_Y_diag[0]):
             dists.append(_perstot_autodiff(Y_orig[pairs_Y_diag], order, internal_p))
         dists = [dist.reshape(1) for dist in dists]
         return ep.concatenate(dists).norms.lp(order).raw
diff --git a/src/python/include/Simplex_tree_interface.h b/src/python/include/Simplex_tree_interface.h
index 56d7c41d..e288a8cf 100644
--- a/src/python/include/Simplex_tree_interface.h
+++ b/src/python/include/Simplex_tree_interface.h
@@ -15,10 +15,13 @@
 #include <gudhi/distance_functions.h>
 #include <gudhi/Simplex_tree.h>
 #include <gudhi/Points_off_io.h>
+#include <gudhi/Flag_complex_edge_collapser.h>
 
 #include <iostream>
 #include <vector>
 #include <utility>  // std::pair
+#include <tuple>
+#include <iterator>  // for std::distance
 
 namespace Gudhi {
 
@@ -157,6 +160,34 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
     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;
+    for (Simplex_handle sh : Base::skeleton_simplex_range(1)) {
+      if (Base::dimension(sh) == 1) {
+        typename Base::Simplex_vertex_range rg = Base::simplex_vertex_range(sh);
+        auto vit = rg.begin();
+        Vertex_handle v = *vit;
+        Vertex_handle w = *++vit;
+        edges.emplace_back(v, w, Base::filtration(sh));
+      }
+    }
+
+    for (int iteration = 0; iteration < nb_collapse_iteration; iteration++) {
+      edges = Gudhi::collapse::flag_complex_collapse_edges(edges);
+    }
+    Simplex_tree_interface* collapsed_stree_ptr = new Simplex_tree_interface();
+    // Copy the original 0-skeleton
+    for (Simplex_handle sh : Base::skeleton_simplex_range(0)) {
+      collapsed_stree_ptr->insert({*(Base::simplex_vertex_range(sh).begin())}, Base::filtration(sh));
+    }
+    // Insert remaining edges
+    for (auto remaining_edge : edges) {
+      collapsed_stree_ptr->insert({std::get<0>(remaining_edge), std::get<1>(remaining_edge)}, std::get<2>(remaining_edge));
+    }
+    return collapsed_stree_ptr;
+  }
+
   // Iterator over the simplex tree
   Complex_simplex_iterator get_simplices_iterator_begin() {
     // this specific case works because the range is just a pair of iterators - won't work if range was a vector
diff --git a/src/python/test/test_alpha_complex.py b/src/python/test/test_alpha_complex.py
index a4ee260b..814f8289 100755
--- a/src/python/test/test_alpha_complex.py
+++ b/src/python/test/test_alpha_complex.py
@@ -198,8 +198,7 @@ def test_delaunay_complex():
         _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)
+    alpha = gd.AlphaComplex(off_file='alphacomplexdoc.off', precision = precision)
 
     simplex_tree = alpha.create_simplex_tree(default_filtration_value = default_filtration_value)
     assert simplex_tree.dimension() == 2
@@ -207,6 +206,18 @@ def _3d_points_on_a_plane(precision, default_filtration_value):
     assert simplex_tree.num_simplices() == 25
 
 def test_3d_points_on_a_plane():
+    off_file = open("alphacomplexdoc.off", "w")
+    off_file.write("OFF         \n" \
+                   "7 0 0       \n" \
+                   "1.0 1.0  0.0\n" \
+                   "7.0 0.0  0.0\n" \
+                   "4.0 6.0  0.0\n" \
+                   "9.0 6.0  0.0\n" \
+                   "0.0 14.0 0.0\n" \
+                   "2.0 19.0 0.0\n" \
+                   "9.0 17.0 0.0\n"  )
+    off_file.close()
+
     for default_filtration_value in [True, False]:
         for precision in ['fast', 'safe', 'exact']:
             _3d_points_on_a_plane(precision, default_filtration_value)
diff --git a/src/python/test/test_representations.py b/src/python/test/test_representations.py
index 589cee00..e5c211a0 100755
--- a/src/python/test/test_representations.py
+++ b/src/python/test/test_representations.py
@@ -4,6 +4,8 @@ import matplotlib.pyplot as plt
 import numpy as np
 import pytest
 
+from sklearn.cluster import KMeans
+
 
 def test_representations_examples():
     # Disable graphics for testing purposes
@@ -15,6 +17,7 @@ def test_representations_examples():
     return None
 
 
+from gudhi.representations.vector_methods import Atol
 from gudhi.representations.metrics import *
 from gudhi.representations.kernel_methods import *
 
@@ -41,3 +44,17 @@ def test_multiple():
     d2 = WassersteinDistance(order=2, internal_p=2, n_jobs=4).fit(l2).transform(l1)
     print(d1.shape, d2.shape)
     assert d1 == pytest.approx(d2, rel=.02)
+
+
+def test_dummy_atol():
+    a = np.array([[1, 2, 4], [1, 4, 0], [1, 0, 4]])
+    b = np.array([[4, 2, 0], [4, 4, 0], [4, 0, 2]])
+    c = np.array([[3, 2, -1], [1, 2, -1]])
+
+    for weighting_method in ["cloud", "iidproba"]:
+        for contrast in ["gaussian", "laplacian", "indicator"]:
+            atol_vectoriser = Atol(quantiser=KMeans(n_clusters=1, random_state=202006), weighting_method=weighting_method, contrast=contrast)
+            atol_vectoriser.fit([a, b, c])
+            atol_vectoriser(a)
+            atol_vectoriser.transform(X=[a, b, c])
+
diff --git a/src/python/test/test_simplex_tree.py b/src/python/test/test_simplex_tree.py
index 1ca84c10..6f1d01cc 100755
--- a/src/python/test/test_simplex_tree.py
+++ b/src/python/test/test_simplex_tree.py
@@ -341,6 +341,24 @@ def test_simplices_iterator():
         print("filtration is: ", simplex[1])
         assert st.filtration(simplex[0]) == simplex[1]
 
+def test_collapse_edges():
+    st = SimplexTree()
+    
+    assert st.insert([0, 1], filtration=1.0) == True
+    assert st.insert([1, 2], filtration=1.0) == True
+    assert st.insert([2, 3], filtration=1.0) == True
+    assert st.insert([0, 3], filtration=1.0) == True
+    assert st.insert([0, 2], filtration=2.0) == True
+    assert st.insert([1, 3], filtration=2.0) == True
+
+    assert st.num_simplices() == 10
+
+    st.collapse_edges()
+    assert st.num_simplices() == 9
+    assert st.find([1, 3]) == False
+    for simplex in st.get_skeleton(0):
+        assert simplex[1] == 1.
+
 def test_reset_filtration():
     st = SimplexTree()
     
@@ -361,4 +379,3 @@ def test_reset_filtration():
                 assert st.filtration(simplex[0]) >= 1.
             else:
                 assert st.filtration(simplex[0]) == 0.
-