Merge remote-tracking branch 'origin/master' into collapse-pr2

26 files changed, 746 insertions, 250 deletions

diff --git a/.github/next_release.md b/.github/next_release.md
index b90aab33..f8085513 100644
--- a/.github/next_release.md
+++ b/.github/next_release.md
@@ -13,6 +13,9 @@ Below is a list of changes made since GUDHI 3.5.0:
 - [Representations](https://gudhi.inria.fr/python/latest/representations.html#gudhi.representations.vector_methods.BettiCurve)
      - A more flexible Betti curve class capable of computing exact curves
 
+- [Simplex tree](https://gudhi.inria.fr/python/latest/simplex_tree_ref.html)
+     - `__deepcopy__`, `copy` and copy constructors
+
 - Installation
      - Boost ≥ 1.66.0 is now required (was ≥ 1.56.0).
      - Python >= 3.5 and cython >= 0.27 are now required.
diff --git a/.github/workflows/pip-build-windows.yml b/.github/workflows/pip-build-windows.yml
index 954b59d5..30b0bd94 100644
--- a/.github/workflows/pip-build-windows.yml
+++ b/.github/workflows/pip-build-windows.yml
@@ -30,14 +30,14 @@ jobs:
         run: |
           mkdir build
           cd ".\build\"
-          cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_TOOLCHAIN_FILE=c:\vcpkg\scripts\buildsystems\vcpkg.cmake -DVCPKG_TARGET_TRIPLET=x64-windows ..
+          cmake -DCMAKE_BUILD_TYPE=Release -DFORCE_EIGEN_DEFAULT_DENSE_INDEX_TYPE_TO_INT=ON -DCMAKE_TOOLCHAIN_FILE=c:\vcpkg\scripts\buildsystems\vcpkg.cmake -DVCPKG_TARGET_TRIPLET=x64-windows ..
           Get-Location
           dir
           cd ".\src\python\"
-          cp "C:\vcpkg\installed\x64-windows\bin\mpfr-6.dll" ".\gudhi\"
-          cp "C:\vcpkg\installed\x64-windows\bin\gmp.dll" ".\gudhi\"
+          cp "C:\vcpkg\installed\x64-windows\bin\mpfr*.dll" ".\gudhi\"
+          cp "C:\vcpkg\installed\x64-windows\bin\gmp*.dll" ".\gudhi\"
           python setup.py bdist_wheel
-          ls dist
+          ls ".\dist\"
           cd ".\dist\"
           Get-ChildItem *.whl | ForEach-Object{python -m pip install --user $_.Name}
       - name: Test python wheel
diff --git a/.github/workflows/pip-packaging-windows.yml b/.github/workflows/pip-packaging-windows.yml
index 962ae68a..142a114c 100644
--- a/.github/workflows/pip-packaging-windows.yml
+++ b/.github/workflows/pip-packaging-windows.yml
@@ -33,14 +33,14 @@ jobs:
         run: |
           mkdir build
           cd ".\build\"
-          cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_TOOLCHAIN_FILE=c:\vcpkg\scripts\buildsystems\vcpkg.cmake -DVCPKG_TARGET_TRIPLET=x64-windows ..
+          cmake -DCMAKE_BUILD_TYPE=Release -DFORCE_EIGEN_DEFAULT_DENSE_INDEX_TYPE_TO_INT=ON -DCMAKE_TOOLCHAIN_FILE=c:\vcpkg\scripts\buildsystems\vcpkg.cmake -DVCPKG_TARGET_TRIPLET=x64-windows ..
           Get-Location
           dir
           cd ".\src\python\"
-          cp "C:\vcpkg\installed\x64-windows\bin\mpfr-6.dll" ".\gudhi\"
-          cp "C:\vcpkg\installed\x64-windows\bin\gmp.dll" ".\gudhi\"
+          cp "C:\vcpkg\installed\x64-windows\bin\mpfr*.dll" ".\gudhi\"
+          cp "C:\vcpkg\installed\x64-windows\bin\gmp*.dll" ".\gudhi\"
           python setup.py bdist_wheel
-          ls dist
+          ls ".\dist\"
           cd ".\dist\"
           Get-ChildItem *.whl | ForEach-Object{python -m pip install --user $_.Name}
       - name: Test python wheel
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 21664244..31264c37 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -5,7 +5,7 @@ jobs:
     timeoutInMinutes: 0
     cancelTimeoutInMinutes: 60
     pool:
-      vmImage: macOS-10.15
+      vmImage: macOS-latest
     variables:
       pythonVersion: '3.7'
       cmakeBuildType: Release
@@ -30,7 +30,7 @@ jobs:
     - bash: |
         mkdir build
         cd build
-        cmake -DCMAKE_BUILD_TYPE:STRING=$(cmakeBuildType) -DWITH_GUDHI_TEST=ON -DWITH_GUDHI_UTILITIES=ON -DWITH_GUDHI_PYTHON=ON ..
+        cmake -DCMAKE_BUILD_TYPE:STRING=$(cmakeBuildType) -DWITH_GUDHI_EXAMPLE=ON -DWITH_GUDHI_TEST=ON -DWITH_GUDHI_UTILITIES=ON -DWITH_GUDHI_PYTHON=ON ..
         make
         make doxygen
         ctest --output-on-failure
@@ -64,20 +64,27 @@ jobs:
         vcpkg install boost-filesystem:x64-windows boost-test:x64-windows boost-program-options:x64-windows tbb:x64-windows eigen3:x64-windows cgal:x64-windows
       displayName: 'Install build dependencies'
     - script: |
-        call "C:\Program Files (x86)\Microsoft Visual Studio\2019\Enterprise\VC\Auxiliary\Build\vcvarsall.bat" amd64
+        call "C:\Program Files\Microsoft Visual Studio\2022\Enterprise\VC\Auxiliary\Build\vcvarsall.bat" amd64
+        IF %errorlevel% NEQ 0 exit /b %errorlevel%
         mkdir build
         cd build
-        cmake -G "Visual Studio 16 2019" -A x64 -DCMAKE_BUILD_TYPE=Release $(cmakeVcpkgFlags) $(cmakeFlags) ..
+        cmake -G "Visual Studio 17 2022" -A x64 -DCMAKE_BUILD_TYPE=Release -DFORCE_EIGEN_DEFAULT_DENSE_INDEX_TYPE_TO_INT=ON $(cmakeVcpkgFlags) $(cmakeFlags) ..
+        IF %errorlevel% NEQ 0 exit /b %errorlevel%
         MSBuild GUDHIdev.sln /m /p:Configuration=Release /p:Platform=x64
+        IF %errorlevel% NEQ 0 exit /b %errorlevel%
         ctest --output-on-failure -C Release -E diff_files
+        IF %errorlevel% NEQ 0 exit /b %errorlevel%
         cmake  -DWITH_GUDHI_PYTHON=ON .
+        IF %errorlevel% NEQ 0 exit /b %errorlevel%
         cd src\python
-        copy "C:\vcpkg\installed\x64-windows\bin\mpfr-6.dll" ".\gudhi\"
-        copy "C:\vcpkg\installed\x64-windows\bin\gmp.dll" ".\gudhi\"
+        copy "C:\vcpkg\installed\x64-windows\bin\mpfr*.dll" ".\gudhi\"
+        copy "C:\vcpkg\installed\x64-windows\bin\gmp*.dll" ".\gudhi\"
         copy "C:\vcpkg\installed\x64-windows\bin\tbb.dll" ".\gudhi\"
         copy "C:\vcpkg\installed\x64-windows\bin\tbbmalloc.dll" ".\gudhi\"
         python setup.py build_ext --inplace
+        IF %errorlevel% NEQ 0 exit /b %errorlevel%
         SET PYTHONPATH=%CD%;%PYTHONPATH%
         echo %PYTHONPATH%
         ctest --output-on-failure -C Release
+        IF %errorlevel% NEQ 0 exit /b %errorlevel%
       displayName: 'Build and test'
diff --git a/biblio/how_to_cite_gudhi.bib.in b/biblio/how_to_cite_gudhi.bib.in
index 54d10857..579dbf41 100644
--- a/biblio/how_to_cite_gudhi.bib.in
+++ b/biblio/how_to_cite_gudhi.bib.in
@@ -78,7 +78,7 @@
 }
 
 @incollection{gudhi:SubSampling
-, author =  "Cl\'ement Jamin, Siargey Kachanovich"
+, author =  "Cl\'ement Jamin and Siargey Kachanovich"
 , title =   "Subsampling"
 , publisher =  "{GUDHI Editorial Board}"
 , edition =     "{@GUDHI_VERSION@}"
@@ -108,7 +108,7 @@
 }
 
 @incollection{gudhi:RipsComplex
-, author =  "Cl\'ement Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse"
+, author =  "Cl\'ement Maria and Pawel Dlotko and Vincent Rouvreau and Marc Glisse"
 , title =   "Rips complex"
 , publisher =  "{GUDHI Editorial Board}"
 , edition =     "{@GUDHI_VERSION@}"
@@ -158,7 +158,7 @@
 }
 
 @incollection{gudhi:Collapse
-, author =  "Siddharth Pritam"
+, author =  "Siddharth Pritam and Marc Glisse"
 , title =   "Edge collapse"
 , publisher =  "{GUDHI Editorial Board}"
 , edition =     "{@GUDHI_VERSION@}"
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
index df5c630e..b3dbc9bb 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h
@@ -57,8 +57,6 @@ namespace Gudhi {
 
 namespace alpha_complex {
 
-thread_local double RELATIVE_PRECISION_OF_TO_DOUBLE = 0.00001;
-
 // Value_from_iterator returns the filtration value from an iterator on alpha shapes values
 //
 // FAST                         SAFE                         EXACT
diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree.h b/src/Simplex_tree/include/gudhi/Simplex_tree.h
index 85790baf..d48f6616 100644
--- a/src/Simplex_tree/include/gudhi/Simplex_tree.h
+++ b/src/Simplex_tree/include/gudhi/Simplex_tree.h
@@ -1283,6 +1283,7 @@ class Simplex_tree {
         Siblings * new_sib = new Siblings(siblings,  // oncles
                                           simplex->first,  // parent
                                           boost::adaptors::reverse(intersection));  // boost::container::ordered_unique_range_t
+        simplex->second.assign_children(new_sib);
         std::vector<Vertex_handle> blocked_new_sib_vertex_list;
         // As all intersections are inserted, we can call the blocker function on all new_sib members
         for (auto new_sib_member = new_sib->members().begin();
@@ -1305,7 +1306,6 @@ class Simplex_tree {
             new_sib->members().erase(blocked_new_sib_member);
           }
           // ensure recursive call
-          simplex->second.assign_children(new_sib);
           siblings_expansion_with_blockers(new_sib, max_dim, k - 1, block_simplex);
         }
       } else {
diff --git a/src/Simplex_tree/test/CMakeLists.txt b/src/Simplex_tree/test/CMakeLists.txt
index cf2b0153..25b562e0 100644
--- a/src/Simplex_tree/test/CMakeLists.txt
+++ b/src/Simplex_tree/test/CMakeLists.txt
@@ -34,3 +34,9 @@ if (TBB_FOUND)
   target_link_libraries(Simplex_tree_make_filtration_non_decreasing_test_unit ${TBB_LIBRARIES})
 endif()
 gudhi_add_boost_test(Simplex_tree_make_filtration_non_decreasing_test_unit)
+
+add_executable ( Simplex_tree_graph_expansion_test_unit simplex_tree_graph_expansion_unit_test.cpp )
+if (TBB_FOUND)
+  target_link_libraries(Simplex_tree_graph_expansion_test_unit ${TBB_LIBRARIES})
+endif()
+gudhi_add_boost_test(Simplex_tree_graph_expansion_test_unit)
diff --git a/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp b/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp
index 881a06ae..6d63d8ae 100644
--- a/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp
+++ b/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp
@@ -9,33 +9,62 @@
  */
 
 #include <iostream>
-#include <fstream>
-#include <string>
-#include <algorithm>
-#include <utility> // std::pair, std::make_pair
-#include <cmath> // float comparison
-#include <limits>
-#include <functional> // greater
+#include <vector>
 
 #define BOOST_TEST_DYN_LINK
-#define BOOST_TEST_MODULE "simplex_tree"
+#define BOOST_TEST_MODULE "simplex_tree_graph_expansion"
 #include <boost/test/unit_test.hpp>
 #include <boost/mpl/list.hpp>
 
-//  ^
-// /!\ Nothing else from Simplex_tree shall be included to test includes are well defined.
 #include "gudhi/Simplex_tree.h"
+#include <gudhi/Unitary_tests_utils.h>
 
 using namespace Gudhi;
 
 typedef boost::mpl::list<Simplex_tree<>, Simplex_tree<Simplex_tree_options_fast_persistence>> list_of_tested_variants;
 
+BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_all_is_blocked, typeST, list_of_tested_variants) {
+  std::clog << "********************************************************************\n";
+  std::clog << "simplex_tree_expansion_all_is_blocked\n";
+  std::clog << "********************************************************************\n";
+  using Simplex_handle = typename typeST::Simplex_handle;
+  // Construct the Simplex Tree with a 1-skeleton graph example
+  typeST simplex_tree;
+
+  simplex_tree.insert_simplex({0, 1}, 0.);
+  simplex_tree.insert_simplex({0, 2}, 1.);
+  simplex_tree.insert_simplex({0, 3}, 2.);
+  simplex_tree.insert_simplex({1, 2}, 3.);
+  simplex_tree.insert_simplex({1, 3}, 4.);
+  simplex_tree.insert_simplex({2, 3}, 5.);
+  simplex_tree.insert_simplex({2, 4}, 6.);
+  simplex_tree.insert_simplex({3, 6}, 7.);
+  simplex_tree.insert_simplex({4, 5}, 8.);
+  simplex_tree.insert_simplex({4, 6}, 9.);
+  simplex_tree.insert_simplex({5, 6}, 10.);
+  simplex_tree.insert_simplex({6}, 10.);
 
-bool AreAlmostTheSame(float a, float b) {
-  return std::fabs(a - b) < std::numeric_limits<float>::epsilon();
+  typeST stree_copy = simplex_tree;
+
+  simplex_tree.expansion_with_blockers(3, [&](Simplex_handle sh){ return true; });
+
+  std::clog << "* The complex contains " << simplex_tree.num_simplices() << " simplices";
+  std::clog << " - dimension " << simplex_tree.dimension() << "\n";
+  std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
+  for (auto f_simplex : simplex_tree.filtration_simplex_range()) {
+    std::clog << "   " << "[" << simplex_tree.filtration(f_simplex) << "] ";
+    for (auto vertex : simplex_tree.simplex_vertex_range(f_simplex))
+      std::clog << "(" << vertex << ")";
+    std::clog << std::endl;
+  }
+
+  BOOST_CHECK(stree_copy == simplex_tree);
 }
 
 BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_3, typeST, list_of_tested_variants) {
+  std::clog << "********************************************************************\n";
+  std::clog << "simplex_tree_expansion_with_blockers_3\n";
+  std::clog << "********************************************************************\n";
   using Simplex_handle = typename typeST::Simplex_handle;
   // Construct the Simplex Tree with a 1-skeleton graph example
   typeST simplex_tree;
@@ -72,9 +101,6 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_3, typeST, li
       return result;
     });
 
-  std::clog << "********************************************************************\n";
-  std::clog << "simplex_tree_expansion_with_blockers_3\n";
-  std::clog << "********************************************************************\n";
   std::clog << "* The complex contains " << simplex_tree.num_simplices() << " simplices";
   std::clog << " - dimension " << simplex_tree.dimension() << "\n";
   std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
@@ -89,15 +115,23 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_3, typeST, li
   BOOST_CHECK(simplex_tree.dimension() == 3);
   // {4, 5, 6} shall be blocked
   BOOST_CHECK(simplex_tree.find({4, 5, 6}) == simplex_tree.null_simplex());
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,2})), 4.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,3})), 5.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,2,3})), 6.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({1,2,3})), 6.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,2,3})), 7.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,2})),
+                                                          static_cast<typename typeST::Filtration_value>(4.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,3})),
+                                                          static_cast<typename typeST::Filtration_value>(5.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(6.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({1,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(6.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(7.));
 
 }
 
 BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_2, typeST, list_of_tested_variants) {
+  std::clog << "********************************************************************\n";
+  std::clog << "simplex_tree_expansion_with_blockers_2\n";
+  std::clog << "********************************************************************\n";
   using Simplex_handle = typename typeST::Simplex_handle;
   // Construct the Simplex Tree with a 1-skeleton graph example
   typeST simplex_tree;
@@ -134,9 +168,6 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_2, typeST, li
       return result;
     });
 
-  std::clog << "********************************************************************\n";
-  std::clog << "simplex_tree_expansion_with_blockers_2\n";
-  std::clog << "********************************************************************\n";
   std::clog << "* The complex contains " << simplex_tree.num_simplices() << " simplices";
   std::clog << " - dimension " << simplex_tree.dimension() << "\n";
   std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
@@ -151,14 +182,22 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_2, typeST, li
   BOOST_CHECK(simplex_tree.dimension() == 2);
   // {4, 5, 6} shall be blocked
   BOOST_CHECK(simplex_tree.find({4, 5, 6}) == simplex_tree.null_simplex());
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,2})), 4.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,3})), 5.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,2,3})), 6.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({1,2,3})), 6.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,2})),
+                                                          static_cast<typename typeST::Filtration_value>(4.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,3})),
+                                                          static_cast<typename typeST::Filtration_value>(5.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(6.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({1,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(6.));
   BOOST_CHECK(simplex_tree.find({0,1,2,3}) == simplex_tree.null_simplex());
 }
 
-BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion, typeST, list_of_tested_variants) {
+BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_find_simplex_blockers, typeST, list_of_tested_variants) {
+  std::clog << "********************************************************************\n";
+  std::clog << "simplex_tree_expansion_with_find_simplex_blockers\n";
+  std::clog << "********************************************************************\n";
+  using Simplex_handle = typename typeST::Simplex_handle;
   // Construct the Simplex Tree with a 1-skeleton graph example
   typeST simplex_tree;
 
@@ -175,10 +214,66 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion, typeST, list_of_tested_var
   simplex_tree.insert_simplex({5, 6}, 10.);
   simplex_tree.insert_simplex({6}, 10.);
 
-  simplex_tree.expansion(3);
+  simplex_tree.expansion_with_blockers(3, [&](Simplex_handle sh){
+      bool result = false;
+      std::clog << "Blocker on [";
+      std::vector<typename typeST::Vertex_handle> simplex;
+      // User can loop on the vertices from the given simplex_handle i.e.
+      for (auto vertex : simplex_tree.simplex_vertex_range(sh)) {
+        // We block the expansion, if the vertex '1' is in the given list of vertices
+        if (vertex == 1)
+          result = true;
+        std::clog << vertex << ", ";
+        simplex.push_back(vertex);
+      }
+      std::clog << "] => " << result << std::endl;
+      // Not efficient but test it works - required by the python interface
+      BOOST_CHECK(simplex_tree.find(simplex) == sh);
+      return result;
+    });
+
+  std::clog << "* The complex contains " << simplex_tree.num_simplices() << " simplices";
+  std::clog << " - dimension " << simplex_tree.dimension() << "\n";
+  std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
+  for (auto f_simplex : simplex_tree.filtration_simplex_range()) {
+    std::clog << "   " << "[" << simplex_tree.filtration(f_simplex) << "] ";
+    for (auto vertex : simplex_tree.simplex_vertex_range(f_simplex))
+      std::clog << "(" << vertex << ")";
+    std::clog << std::endl;
+  }
+
+  BOOST_CHECK(simplex_tree.num_simplices() == 20);
+  BOOST_CHECK(simplex_tree.dimension() == 2);
+
+  // {1, 2, 3}, {0, 1, 2} and {0, 1, 3} shall be blocked as it contains vertex 1
+  BOOST_CHECK(simplex_tree.find({4, 5, 6}) != simplex_tree.null_simplex());
+  BOOST_CHECK(simplex_tree.find({1, 2, 3}) == simplex_tree.null_simplex());
+  BOOST_CHECK(simplex_tree.find({0, 2, 3}) != simplex_tree.null_simplex());
+  BOOST_CHECK(simplex_tree.find({0, 1, 2}) == simplex_tree.null_simplex());
+  BOOST_CHECK(simplex_tree.find({0, 1, 3}) == simplex_tree.null_simplex());
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_3, typeST, list_of_tested_variants) {
   std::clog << "********************************************************************\n";
   std::clog << "simplex_tree_expansion_3\n";
   std::clog << "********************************************************************\n";
+  // Construct the Simplex Tree with a 1-skeleton graph example
+  typeST simplex_tree;
+
+  simplex_tree.insert_simplex({0, 1}, 0.);
+  simplex_tree.insert_simplex({0, 2}, 1.);
+  simplex_tree.insert_simplex({0, 3}, 2.);
+  simplex_tree.insert_simplex({1, 2}, 3.);
+  simplex_tree.insert_simplex({1, 3}, 4.);
+  simplex_tree.insert_simplex({2, 3}, 5.);
+  simplex_tree.insert_simplex({2, 4}, 6.);
+  simplex_tree.insert_simplex({3, 6}, 7.);
+  simplex_tree.insert_simplex({4, 5}, 8.);
+  simplex_tree.insert_simplex({4, 6}, 9.);
+  simplex_tree.insert_simplex({5, 6}, 10.);
+  simplex_tree.insert_simplex({6}, 10.);
+
+  simplex_tree.expansion(3);
   std::clog << "* The complex contains " << simplex_tree.num_simplices() << " simplices";
   std::clog << " - dimension " << simplex_tree.dimension() << "\n";
   std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
@@ -192,16 +287,25 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion, typeST, list_of_tested_var
   BOOST_CHECK(simplex_tree.num_simplices() == 24);
   BOOST_CHECK(simplex_tree.dimension() == 3);
 
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({4,5,6})), 10.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,2})), 3.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,3})), 4.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,2,3})), 5.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({1,2,3})), 5.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,2,3})), 5.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({4,5,6})),
+                                                          static_cast<typename typeST::Filtration_value>(10.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,2})),
+                                                          static_cast<typename typeST::Filtration_value>(3.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,3})),
+                                                          static_cast<typename typeST::Filtration_value>(4.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(5.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({1,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(5.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(5.));
 
 }
 
 BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_2, typeST, list_of_tested_variants) {
+  std::clog << "********************************************************************\n";
+  std::clog << "simplex_tree_expansion_2\n";
+  std::clog << "********************************************************************\n";
   // Construct the Simplex Tree with a 1-skeleton graph example
   typeST simplex_tree;
 
@@ -220,9 +324,6 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_2, typeST, list_of_tested_v
 
   simplex_tree.expansion(2);
 
-  std::clog << "********************************************************************\n";
-  std::clog << "simplex_tree_expansion_2\n";
-  std::clog << "********************************************************************\n";
   std::clog << "* The complex contains " << simplex_tree.num_simplices() << " simplices";
   std::clog << " - dimension " << simplex_tree.dimension() << "\n";
   std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
@@ -236,10 +337,15 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_2, typeST, list_of_tested_v
   BOOST_CHECK(simplex_tree.num_simplices() == 23);
   BOOST_CHECK(simplex_tree.dimension() == 2);
 
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({4,5,6})), 10.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,2})), 3.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,1,3})), 4.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({0,2,3})), 5.));
-  BOOST_CHECK(AreAlmostTheSame(simplex_tree.filtration(simplex_tree.find({1,2,3})), 5.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({4,5,6})),
+                                                          static_cast<typename typeST::Filtration_value>(10.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,2})),
+                                                          static_cast<typename typeST::Filtration_value>(3.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,1,3})),
+                                                          static_cast<typename typeST::Filtration_value>(4.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({0,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(5.));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(simplex_tree.filtration(simplex_tree.find({1,2,3})),
+                                                          static_cast<typename typeST::Filtration_value>(5.));
   BOOST_CHECK(simplex_tree.find({0,1,2,3}) == simplex_tree.null_simplex());
 }
diff --git a/src/Tangential_complex/benchmark/benchmark_tc.cpp b/src/Tangential_complex/benchmark/benchmark_tc.cpp
index 6da1425f..8e7c72ff 100644
--- a/src/Tangential_complex/benchmark/benchmark_tc.cpp
+++ b/src/Tangential_complex/benchmark/benchmark_tc.cpp
@@ -33,6 +33,7 @@ const std::size_t ONLY_LOAD_THE_FIRST_N_POINTS = 20000000;
 #include <gudhi/sparsify_point_set.h>
 #include <gudhi/random_point_generators.h>
 #include <gudhi/Tangential_complex/utilities.h>
+#include <gudhi/Simplex_tree.h>
 
 #include <CGAL/assertions_behaviour.h>
 #include <CGAL/Epick_d.h>
diff --git a/src/Tangential_complex/example/example_basic.cpp b/src/Tangential_complex/example/example_basic.cpp
index ab35edf0..c50b9b8c 100644
--- a/src/Tangential_complex/example/example_basic.cpp
+++ b/src/Tangential_complex/example/example_basic.cpp
@@ -1,7 +1,6 @@
 #include <gudhi/Tangential_complex.h>
 #include <gudhi/sparsify_point_set.h>
-//#include <gudhi/Fake_simplex_tree.h>
-
+#include <gudhi/Simplex_tree.h>
 
 #include <CGAL/Epick_d.h>
 #include <CGAL/Random.h>
@@ -39,7 +38,6 @@ int main(void) {
 
   // Export the TC into a Simplex_tree
   Gudhi::Simplex_tree<> stree;
-  //Gudhi::Fake_simplex_tree stree;
   tc.create_complex(stree);
 
   // Display stats about inconsistencies
diff --git a/src/Tangential_complex/example/example_with_perturb.cpp b/src/Tangential_complex/example/example_with_perturb.cpp
index d0d877ea..e70e2980 100644
--- a/src/Tangential_complex/example/example_with_perturb.cpp
+++ b/src/Tangential_complex/example/example_with_perturb.cpp
@@ -1,5 +1,6 @@
 #include <gudhi/Tangential_complex.h>
 #include <gudhi/sparsify_point_set.h>
+#include <gudhi/Simplex_tree.h>
 
 #include <CGAL/Epick_d.h>
 #include <CGAL/Random.h>
diff --git a/src/Tangential_complex/test/test_tangential_complex.cpp b/src/Tangential_complex/test/test_tangential_complex.cpp
index 023c1e1a..a24b9ae2 100644
--- a/src/Tangential_complex/test/test_tangential_complex.cpp
+++ b/src/Tangential_complex/test/test_tangential_complex.cpp
@@ -14,6 +14,7 @@
 
 #include <gudhi/Tangential_complex.h>
 #include <gudhi/sparsify_point_set.h>
+#include <gudhi/Simplex_tree.h>
 
 #include <CGAL/Epick_d.h>
 #include <CGAL/Random.h>
diff --git a/src/cmake/modules/GUDHI_third_party_libraries.cmake b/src/cmake/modules/GUDHI_third_party_libraries.cmake
index 7c982b3b..6a94d1f5 100644
--- a/src/cmake/modules/GUDHI_third_party_libraries.cmake
+++ b/src/cmake/modules/GUDHI_third_party_libraries.cmake
@@ -19,6 +19,15 @@ if(GMP_FOUND)
   endif()
 endif()
 
+# from windows vcpkg eigen 3.4.0#2 : build fails with
+# error C2440: '<function-style-cast>': cannot convert from 'Eigen::EigenBase<Derived>::Index' to '__gmp_expr<mpq_t,mpq_t>'
+# cf. https://gitlab.com/libeigen/eigen/-/issues/2476
+# Workaround is to compile with '-DEIGEN_DEFAULT_DENSE_INDEX_TYPE=int'
+if (FORCE_EIGEN_DEFAULT_DENSE_INDEX_TYPE_TO_INT)
+  message("++ User explicit demand to force EIGEN_DEFAULT_DENSE_INDEX_TYPE to int")
+  add_definitions(-DEIGEN_DEFAULT_DENSE_INDEX_TYPE=int)
+endif()
+
 # In CMakeLists.txt, when include(${CGAL_USE_FILE}), CMAKE_CXX_FLAGS are overwritten.
 # cf. http://doc.cgal.org/latest/Manual/installation.html#title40
 # A workaround is to include(${CGAL_USE_FILE}) before adding "-std=c++11".
diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt
index 0b51df41..54221151 100644
--- a/src/python/CMakeLists.txt
+++ b/src/python/CMakeLists.txt
@@ -176,6 +176,15 @@ if(PYTHONINTERP_FOUND)
       set(GUDHI_CYTHON_MODULES "${GUDHI_CYTHON_MODULES}'alpha_complex', ")
     endif ()
 
+    # from windows vcpkg eigen 3.4.0#2 : build fails with
+    # error C2440: '<function-style-cast>': cannot convert from 'Eigen::EigenBase<Derived>::Index' to '__gmp_expr<mpq_t,mpq_t>'
+    # cf. https://gitlab.com/libeigen/eigen/-/issues/2476
+    # Workaround is to compile with '-DEIGEN_DEFAULT_DENSE_INDEX_TYPE=int'
+    if (FORCE_EIGEN_DEFAULT_DENSE_INDEX_TYPE_TO_INT)
+      set(GUDHI_PYTHON_EXTRA_COMPILE_ARGS "${GUDHI_PYTHON_EXTRA_COMPILE_ARGS}'-DEIGEN_DEFAULT_DENSE_INDEX_TYPE=int', ")
+    endif()
+
+
     add_gudhi_debug_info("Boost version ${Boost_VERSION}")
     if(CGAL_FOUND)
       if(NOT CGAL_VERSION VERSION_LESS 5.3.0)
@@ -211,13 +220,14 @@ if(PYTHONINTERP_FOUND)
         endif(NOT GMP_LIBRARIES_DIR)
         add_GUDHI_PYTHON_lib_dir(${GMP_LIBRARIES_DIR})
         message("** Add gmp ${GMP_LIBRARIES_DIR}")
+        # When FORCE_CGAL_NOT_TO_BUILD_WITH_GMPXX is set, not defining CGAL_USE_GMPXX is sufficient enough
         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("${GMPXX_LIBRARIES}")
           add_GUDHI_PYTHON_lib_dir(${GMPXX_LIBRARIES_DIR})
           message("** Add gmpxx ${GMPXX_LIBRARIES_DIR}")
-        endif(GMPXX_FOUND)
+        endif()
       endif(GMP_FOUND)
       if(MPFR_FOUND)
         add_gudhi_debug_info("MPFR_LIBRARIES = ${MPFR_LIBRARIES}")
@@ -581,6 +591,10 @@ if(PYTHONINTERP_FOUND)
       add_gudhi_py_test(test_dtm_rips_complex)
     endif()
 
+    # persistence graphical tools
+    if(MATPLOTLIB_FOUND)
+      add_gudhi_py_test(test_persistence_graphical_tools)
+    endif()
 
     # Set missing or not modules
     set(GUDHI_MODULES ${GUDHI_MODULES} "python" CACHE INTERNAL "GUDHI_MODULES")
diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst
index cfd22742..b060c86e 100644
--- a/src/python/doc/alpha_complex_user.rst
+++ b/src/python/doc/alpha_complex_user.rst
@@ -27,7 +27,8 @@ Remarks
   If you pass :code:`precision = 'exact'` to :func:`~gudhi.AlphaComplex.__init__`, the filtration values are the exact
   ones converted to float. This can be very slow.
   If you pass :code:`precision = 'safe'` (the default), the filtration values are only
-  guaranteed to have a small multiplicative error compared to the exact value.
+  guaranteed to have a small multiplicative error compared to the exact value, see
+  :func:`~gudhi.AlphaComplex.set_float_relative_precision` to modify the precision.
   A drawback, when computing persistence, is that an empty exact interval [10^12,10^12] may become a
   non-empty approximate interval [10^12,10^12+10^6].
   Using :code:`precision = 'fast'` makes the computations slightly faster, and the combinatorics are still exact, but
diff --git a/src/python/doc/persistence_graphical_tools_user.rst b/src/python/doc/persistence_graphical_tools_user.rst
index d95b9d2b..e1d28c71 100644
--- a/src/python/doc/persistence_graphical_tools_user.rst
+++ b/src/python/doc/persistence_graphical_tools_user.rst
@@ -60,7 +60,7 @@ of shape (N x 2) encoding a persistence diagram (in a given dimension).
     import matplotlib.pyplot as plt
     import gudhi
     import numpy as np
-    d = np.array([[0, 1], [1, 2], [1, np.inf]])
+    d = np.array([[0., 1.], [1., 2.], [1., np.inf]])
     gudhi.plot_persistence_diagram(d)
     plt.show()
 
diff --git a/src/python/gudhi/alpha_complex.pyx b/src/python/gudhi/alpha_complex.pyx
index a4888914..375e1561 100644
--- a/src/python/gudhi/alpha_complex.pyx
+++ b/src/python/gudhi/alpha_complex.pyx
@@ -31,6 +31,10 @@ cdef extern from "Alpha_complex_interface.h" namespace "Gudhi":
         Alpha_complex_interface(vector[vector[double]] points, vector[double] weights, 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 default_filtration_value) nogil except +
+        @staticmethod
+        void set_float_relative_precision(double precision) nogil
+        @staticmethod
+        double get_float_relative_precision() nogil
 
 # AlphaComplex python interface
 cdef class AlphaComplex:
@@ -133,3 +137,28 @@ cdef class AlphaComplex:
             self.this_ptr.create_simplex_tree(<Simplex_tree_interface_full_featured*>stree_int_ptr,
                                               mas, compute_filtration)
         return stree
+
+    @staticmethod
+    def set_float_relative_precision(precision):
+        """
+        :param precision: When the AlphaComplex is constructed with :code:`precision = 'safe'` (the default),
+            one can set the float relative precision of filtration values computed in
+            :func:`~gudhi.AlphaComplex.create_simplex_tree`.
+            Default is :code:`1e-5` (cf. :func:`~gudhi.AlphaComplex.get_float_relative_precision`).
+            For more details, please refer to
+            `CGAL::Lazy_exact_nt<NT>::set_relative_precision_of_to_double <https://doc.cgal.org/latest/Number_types/classCGAL_1_1Lazy__exact__nt.html>`_
+        :type precision: float
+        """
+        if precision <=0. or precision >= 1.:
+            raise ValueError("Relative precision value must be strictly greater than 0 and strictly lower than 1")
+        Alpha_complex_interface.set_float_relative_precision(precision)
+    
+    @staticmethod
+    def get_float_relative_precision():
+        """
+        :returns: The float relative precision of filtration values computation in
+            :func:`~gudhi.AlphaComplex.create_simplex_tree` when the AlphaComplex is constructed with
+            :code:`precision = 'safe'` (the default).
+        :rtype: float
+        """
+        return Alpha_complex_interface.get_float_relative_precision()
diff --git a/src/python/gudhi/persistence_graphical_tools.py b/src/python/gudhi/persistence_graphical_tools.py
index 848dc03e..7ed11360 100644
--- a/src/python/gudhi/persistence_graphical_tools.py
+++ b/src/python/gudhi/persistence_graphical_tools.py
@@ -12,6 +12,9 @@ from os import path
 from math import isfinite
 import numpy as np
 from functools import lru_cache
+import warnings
+import errno
+import os
 
 from gudhi.reader_utils import read_persistence_intervals_in_dimension
 from gudhi.reader_utils import read_persistence_intervals_grouped_by_dimension
@@ -22,6 +25,7 @@ __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.
 
@@ -44,20 +48,46 @@ def __min_birth_max_death(persistence, band=0.0):
             min_birth = float(interval[1][0])
     if band > 0.0:
         max_death += band
+    # can happen if only points at inf death
+    if min_birth == max_death:
+        max_death = max_death + 1.0
     return (min_birth, max_death)
 
 
 def _array_handler(a):
-    '''
+    """
     :param a: if array, assumes it is a (n x 2) np.array and return a
                 persistence-compatible list (padding with 0), so that the
                 plot can be performed seamlessly.
-    '''
-    if isinstance(a[0][1], np.float64) or isinstance(a[0][1], float):
+    """
+    if isinstance(a[0][1], (np.floating, float)):
         return [[0, x] for x in a]
     else:
         return a
 
+
+def _limit_to_max_intervals(persistence, max_intervals, key):
+    """This function returns truncated persistence if length is bigger than max_intervals.
+    :param persistence: Persistence intervals values list. Can be grouped by dimension or not.
+    :type persistence: an array of (dimension, array of (birth, death)) or an array of (birth, death).
+    :param max_intervals: maximal number of intervals to display.
+        Selected intervals are those with the longest life time. Set it
+        to 0 to see all. Default value is 1000.
+    :type max_intervals: int.
+    :param key: key function for sort algorithm.
+    :type key: function or lambda.
+    """
+    if max_intervals > 0 and max_intervals < len(persistence):
+        warnings.warn(
+            "There are %s intervals given as input, whereas max_intervals is set to %s."
+            % (len(persistence), max_intervals)
+        )
+        # Sort by life time, then takes only the max_intervals elements
+        return sorted(persistence, key=key, reverse=True)[:max_intervals]
+    else:
+        return persistence
+
+
 @lru_cache(maxsize=1)
 def _matplotlib_can_use_tex():
     """This function returns True if matplotlib can deal with LaTeX, False otherwise.
@@ -65,17 +95,17 @@ def _matplotlib_can_use_tex():
     """
     try:
         from matplotlib import checkdep_usetex
+
         return checkdep_usetex(True)
-    except ImportError:
-        print("This function is not available, you may be missing matplotlib.")
+    except ImportError as import_error:
+        warnings.warn(f"This function is not available.\nModuleNotFoundError: No module named '{import_error.name}'.")
 
 
 def plot_persistence_barcode(
     persistence=[],
     persistence_file="",
     alpha=0.6,
-    max_intervals=1000,
-    max_barcodes=1000,
+    max_intervals=20000,
     inf_delta=0.1,
     legend=False,
     colormap=None,
@@ -97,7 +127,7 @@ def plot_persistence_barcode(
     :type alpha: float.
     :param max_intervals: maximal number of intervals to display.
         Selected intervals are those with the longest life time. Set it
-        to 0 to see all. Default value is 1000.
+        to 0 to see all. Default value is 20000.
     :type max_intervals: int.
     :param inf_delta: Infinity is placed at :code:`((max_death - min_birth) x
         inf_delta)` above :code:`max_death` value. A reasonable value is
@@ -119,99 +149,68 @@ def plot_persistence_barcode(
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
         from matplotlib import rc
+
         if _gudhi_matplotlib_use_tex and _matplotlib_can_use_tex():
-            plt.rc('text', usetex=True)
-            plt.rc('font', family='serif')
+            plt.rc("text", usetex=True)
+            plt.rc("font", family="serif")
         else:
-            plt.rc('text', usetex=False)
-            plt.rc('font', family='DejaVu Sans')
+            plt.rc("text", usetex=False)
+            plt.rc("font", family="DejaVu Sans")
 
         if persistence_file != "":
             if path.isfile(persistence_file):
                 # Reset persistence
                 persistence = []
-                diag = read_persistence_intervals_grouped_by_dimension(
-                    persistence_file=persistence_file
-                )
+                diag = read_persistence_intervals_grouped_by_dimension(persistence_file=persistence_file)
                 for key in diag.keys():
                     for persistence_interval in diag[key]:
                         persistence.append((key, persistence_interval))
             else:
-                print("file " + persistence_file + " not found.")
-                return None
-
-        persistence = _array_handler(persistence)
-
-        if max_barcodes != 1000:
-            print("Deprecated parameter. It has been replaced by max_intervals")
-            max_intervals = max_barcodes
-
-        if max_intervals > 0 and max_intervals < len(persistence):
-            # Sort by life time, then takes only the max_intervals elements
-            persistence = sorted(
-                persistence,
-                key=lambda life_time: life_time[1][1] - life_time[1][0],
-                reverse=True,
-            )[:max_intervals]
-        
-        if colormap == None:
-            colormap = plt.cm.Set1.colors
-        if axes == None:
-            fig, axes = plt.subplots(1, 1)
+                raise FileNotFoundError(errno.ENOENT, os.strerror(errno.ENOENT), persistence_file)
 
-        persistence = sorted(persistence, key=lambda birth: birth[1][0])
+        try:
+            persistence = _array_handler(persistence)
+            persistence = _limit_to_max_intervals(
+                persistence, max_intervals, key=lambda life_time: life_time[1][1] - life_time[1][0]
+            )
+            (min_birth, max_death) = __min_birth_max_death(persistence)
+            persistence = sorted(persistence, key=lambda birth: birth[1][0])
+        except IndexError:
+            min_birth, max_death = 0.0, 1.0
+            pass
 
-        (min_birth, max_death) = __min_birth_max_death(persistence)
-        ind = 0
         delta = (max_death - min_birth) * inf_delta
         # Replace infinity values with max_death + delta for bar code to be more
         # readable
         infinity = max_death + delta
         axis_start = min_birth - delta
-        # Draw horizontal bars in loop
-        for interval in reversed(persistence):
-            if float(interval[1][1]) != float("inf"):
-                # Finite death case
-                axes.barh(
-                    ind,
-                    (interval[1][1] - interval[1][0]),
-                    height=0.8,
-                    left=interval[1][0],
-                    alpha=alpha,
-                    color=colormap[interval[0]],
-                    linewidth=0,
-                )
-            else:
-                # Infinite death case for diagram to be nicer
-                axes.barh(
-                    ind,
-                    (infinity - interval[1][0]),
-                    height=0.8,
-                    left=interval[1][0],
-                    alpha=alpha,
-                    color=colormap[interval[0]],
-                    linewidth=0,
-                )
-            ind = ind + 1
+
+        if axes == None:
+            _, axes = plt.subplots(1, 1)
+        if colormap == None:
+            colormap = plt.cm.Set1.colors
+
+        x=[birth for (dim,(birth,death)) in persistence]
+        y=[(death - birth) if death != float("inf") else (infinity - birth) for (dim,(birth,death)) in persistence]
+        c=[colormap[dim] for (dim,(birth,death)) in persistence]
+
+        axes.barh(list(reversed(range(len(x)))), y, height=0.8, left=x, alpha=alpha, color=c, linewidth=0)
 
         if legend:
             dimensions = list(set(item[0] for item in persistence))
             axes.legend(
-                handles=[
-                    mpatches.Patch(color=colormap[dim], label=str(dim))
-                    for dim in dimensions
-                ],
-                loc="lower right",
+                handles=[mpatches.Patch(color=colormap[dim], label=str(dim)) for dim in dimensions], loc="lower right",
             )
 
         axes.set_title("Persistence barcode", fontsize=fontsize)
 
         # Ends plot on infinity value and starts a little bit before min_birth
-        axes.axis([axis_start, infinity, 0, ind])
+        if len(x) != 0:
+            axes.axis([axis_start, infinity, 0, len(x)])
         return axes
 
-    except ImportError:
-        print("This function is not available, you may be missing matplotlib.")
+    except ImportError as import_error:
+        warnings.warn(f"This function is not available.\nModuleNotFoundError: No module named '{import_error.name}'.")
 
 
 def plot_persistence_diagram(
@@ -219,14 +218,13 @@ def plot_persistence_diagram(
     persistence_file="",
     alpha=0.6,
     band=0.0,
-    max_intervals=1000,
-    max_plots=1000,
+    max_intervals=1000000,
     inf_delta=0.1,
     legend=False,
     colormap=None,
     axes=None,
     fontsize=16,
-    greyblock=True
+    greyblock=True,
 ):
     """This function plots the persistence diagram from persistence values
     list, a np.array of shape (N x 2) representing a diagram in a single
@@ -244,7 +242,7 @@ def plot_persistence_diagram(
     :type band: float.
     :param max_intervals: maximal number of intervals to display.
         Selected intervals are those with the longest life time. Set it
-        to 0 to see all. Default value is 1000.
+        to 0 to see all. Default value is 1000000.
     :type max_intervals: int.
     :param inf_delta: Infinity is placed at :code:`((max_death - min_birth) x
         inf_delta)` above :code:`max_death` value. A reasonable value is
@@ -268,47 +266,35 @@ def plot_persistence_diagram(
         import matplotlib.pyplot as plt
         import matplotlib.patches as mpatches
         from matplotlib import rc
+
         if _gudhi_matplotlib_use_tex and _matplotlib_can_use_tex():
-            plt.rc('text', usetex=True)
-            plt.rc('font', family='serif')
+            plt.rc("text", usetex=True)
+            plt.rc("font", family="serif")
         else:
-            plt.rc('text', usetex=False)
-            plt.rc('font', family='DejaVu Sans')
+            plt.rc("text", usetex=False)
+            plt.rc("font", family="DejaVu Sans")
 
         if persistence_file != "":
             if path.isfile(persistence_file):
                 # Reset persistence
                 persistence = []
-                diag = read_persistence_intervals_grouped_by_dimension(
-                    persistence_file=persistence_file
-                )
+                diag = read_persistence_intervals_grouped_by_dimension(persistence_file=persistence_file)
                 for key in diag.keys():
                     for persistence_interval in diag[key]:
                         persistence.append((key, persistence_interval))
             else:
-                print("file " + persistence_file + " not found.")
-                return None
-
-        persistence = _array_handler(persistence)
+                raise FileNotFoundError(errno.ENOENT, os.strerror(errno.ENOENT), persistence_file)
 
-        if max_plots != 1000:
-            print("Deprecated parameter. It has been replaced by max_intervals")
-            max_intervals = max_plots
-
-        if max_intervals > 0 and max_intervals < len(persistence):
-            # Sort by life time, then takes only the max_intervals elements
-            persistence = sorted(
-                persistence,
-                key=lambda life_time: life_time[1][1] - life_time[1][0],
-                reverse=True,
-            )[:max_intervals]
-
-        if colormap == None:
-            colormap = plt.cm.Set1.colors
-        if axes == None:
-            fig, axes = plt.subplots(1, 1)
+        try:
+            persistence = _array_handler(persistence)
+            persistence = _limit_to_max_intervals(
+                persistence, max_intervals, key=lambda life_time: life_time[1][1] - life_time[1][0]
+            )
+            min_birth, max_death = __min_birth_max_death(persistence, band)
+        except IndexError:
+            min_birth, max_death = 0.0, 1.0
+            pass
 
-        (min_birth, max_death) = __min_birth_max_death(persistence, band)
         delta = (max_death - min_birth) * inf_delta
         # Replace infinity values with max_death + delta for diagram to be more
         # readable
@@ -316,61 +302,56 @@ def plot_persistence_diagram(
         axis_end = max_death + delta / 2
         axis_start = min_birth - delta
 
+        if axes == None:
+            _, axes = plt.subplots(1, 1)
+        if colormap == None:
+            colormap = plt.cm.Set1.colors
         # bootstrap band
         if band > 0.0:
             x = np.linspace(axis_start, infinity, 1000)
             axes.fill_between(x, x, x + band, alpha=alpha, facecolor="red")
         # lower diag patch
         if greyblock:
-            axes.add_patch(mpatches.Polygon([[axis_start, axis_start], [axis_end, axis_start], [axis_end, axis_end]], fill=True, color='lightgrey'))
-        # Draw points in loop
-        pts_at_infty = False  # Records presence of pts at infty
-        for interval in reversed(persistence):
-            if float(interval[1][1]) != float("inf"):
-                # Finite death case
-                axes.scatter(
-                    interval[1][0],
-                    interval[1][1],
-                    alpha=alpha,
-                    color=colormap[interval[0]],
+            axes.add_patch(
+                mpatches.Polygon(
+                    [[axis_start, axis_start], [axis_end, axis_start], [axis_end, axis_end]],
+                    fill=True,
+                    color="lightgrey",
                 )
-            else:
-                pts_at_infty = True
-                # Infinite death case for diagram to be nicer
-                axes.scatter(
-                    interval[1][0], infinity, alpha=alpha, color=colormap[interval[0]]
-                )
-        if pts_at_infty:
+            )
+        # line display of equation : birth = death
+        axes.plot([axis_start, axis_end], [axis_start, axis_end], linewidth=1.0, color="k")
+
+        x=[birth for (dim,(birth,death)) in persistence]
+        y=[death if death != float("inf") else infinity for (dim,(birth,death)) in persistence]
+        c=[colormap[dim] for (dim,(birth,death)) in persistence]
+
+        axes.scatter(x,y,alpha=alpha,color=c)
+        if float("inf") in (death for (dim,(birth,death)) in persistence):
             # infinity line and text
-            axes.plot([axis_start, axis_end], [axis_start, axis_end], linewidth=1.0, color="k")
             axes.plot([axis_start, axis_end], [infinity, infinity], linewidth=1.0, color="k", alpha=alpha)
             # Infinity label
             yt = axes.get_yticks()
-            yt = yt[np.where(yt < axis_end)] # to avoid ploting ticklabel higher than infinity
+            yt = yt[np.where(yt < axis_end)]  # to avoid ploting ticklabel higher than infinity
             yt = np.append(yt, infinity)
             ytl = ["%.3f" % e for e in yt]  # to avoid float precision error
-            ytl[-1] = r'$+\infty$'
+            ytl[-1] = r"$+\infty$"
             axes.set_yticks(yt)
             axes.set_yticklabels(ytl)
 
         if legend:
             dimensions = list(set(item[0] for item in persistence))
-            axes.legend(
-                handles=[
-                    mpatches.Patch(color=colormap[dim], label=str(dim))
-                    for dim in dimensions
-                ]
-            )
+            axes.legend(handles=[mpatches.Patch(color=colormap[dim], label=str(dim)) for dim in dimensions])
 
         axes.set_xlabel("Birth", fontsize=fontsize)
         axes.set_ylabel("Death", fontsize=fontsize)
         axes.set_title("Persistence diagram", fontsize=fontsize)
         # Ends plot on infinity value and starts a little bit before min_birth
-        axes.axis([axis_start, axis_end, axis_start, infinity + delta/2])
+        axes.axis([axis_start, axis_end, axis_start, infinity + delta / 2])
         return axes
 
-    except ImportError:
-        print("This function is not available, you may be missing matplotlib.")
+    except ImportError as import_error:
+        warnings.warn(f"This function is not available.\nModuleNotFoundError: No module named '{import_error.name}'.")
 
 
 def plot_persistence_density(
@@ -384,7 +365,7 @@ def plot_persistence_density(
     legend=False,
     axes=None,
     fontsize=16,
-    greyblock=False
+    greyblock=False,
 ):
     """This function plots the persistence density from persistence
     values list, np.array of shape (N x 2) representing a diagram
@@ -444,12 +425,13 @@ def plot_persistence_density(
         import matplotlib.patches as mpatches
         from scipy.stats import kde
         from matplotlib import rc
+
         if _gudhi_matplotlib_use_tex and _matplotlib_can_use_tex():
-            plt.rc('text', usetex=True)
-            plt.rc('font', family='serif')
+            plt.rc("text", usetex=True)
+            plt.rc("font", family="serif")
         else:
-            plt.rc('text', usetex=False)
-            plt.rc('font', family='DejaVu Sans')
+            plt.rc("text", usetex=False)
+            plt.rc("font", family="DejaVu Sans")
 
         if persistence_file != "":
             if dimension is None:
@@ -460,10 +442,16 @@ def plot_persistence_density(
                     persistence_file=persistence_file, only_this_dim=dimension
                 )
             else:
-                print("file " + persistence_file + " not found.")
-                return None
+                raise FileNotFoundError(errno.ENOENT, os.strerror(errno.ENOENT), persistence_file)
+
+        # default cmap value cannot be done at argument definition level as matplotlib is not yet defined.
+        if cmap is None:
+            cmap = plt.cm.hot_r
+        if axes == None:
+            _, axes = plt.subplots(1, 1)
 
-        if len(persistence) > 0:
+        try:
+            # if not read from file but given by an argument
             persistence = _array_handler(persistence)
             persistence_dim = np.array(
                 [
@@ -472,47 +460,54 @@ def plot_persistence_density(
                     if (dim_interval[0] == dimension) or (dimension is None)
                 ]
             )
-
-        persistence_dim = persistence_dim[np.isfinite(persistence_dim[:, 1])]
-        if max_intervals > 0 and max_intervals < len(persistence_dim):
-            # Sort by life time, then takes only the max_intervals elements
+            persistence_dim = persistence_dim[np.isfinite(persistence_dim[:, 1])]
             persistence_dim = np.array(
-                sorted(
-                    persistence_dim,
-                    key=lambda life_time: life_time[1] - life_time[0],
-                    reverse=True,
-                )[:max_intervals]
+                _limit_to_max_intervals(
+                    persistence_dim, max_intervals, key=lambda life_time: life_time[1] - life_time[0]
+                )
             )
 
-        # Set as numpy array birth and death (remove undefined values - inf and NaN)
-        birth = persistence_dim[:, 0]
-        death = persistence_dim[:, 1]
-
-        # default cmap value cannot be done at argument definition level as matplotlib is not yet defined.
-        if cmap is None:
-            cmap = plt.cm.hot_r
-        if axes == None:
-            fig, axes = plt.subplots(1, 1)
+            # Set as numpy array birth and death (remove undefined values - inf and NaN)
+            birth = persistence_dim[:, 0]
+            death = persistence_dim[:, 1]
+            birth_min = birth.min()
+            birth_max = birth.max()
+            death_min = death.min()
+            death_max = death.max()
+
+            # Evaluate a gaussian kde on a regular grid of nbins x nbins over data extents
+            k = kde.gaussian_kde([birth, death], bw_method=bw_method)
+            xi, yi = np.mgrid[
+                birth_min : birth_max : nbins * 1j, death_min : death_max : nbins * 1j,
+            ]
+            zi = k(np.vstack([xi.flatten(), yi.flatten()]))
+            # Make the plot
+            img = axes.pcolormesh(xi, yi, zi.reshape(xi.shape), cmap=cmap, shading="auto")
+            plot_success = True
+
+        # IndexError on empty diagrams, ValueError on only inf death values
+        except (IndexError, ValueError):
+            birth_min = 0.0
+            birth_max = 1.0
+            death_min = 0.0
+            death_max = 1.0
+            plot_success = False
+            pass
 
         # line display of equation : birth = death
-        x = np.linspace(death.min(), birth.max(), 1000)
+        x = np.linspace(death_min, birth_max, 1000)
         axes.plot(x, x, color="k", linewidth=1.0)
 
-        # Evaluate a gaussian kde on a regular grid of nbins x nbins over data extents
-        k = kde.gaussian_kde([birth, death], bw_method=bw_method)
-        xi, yi = np.mgrid[
-            birth.min() : birth.max() : nbins * 1j,
-            death.min() : death.max() : nbins * 1j,
-        ]
-        zi = k(np.vstack([xi.flatten(), yi.flatten()]))
-
-        # Make the plot
-        img = axes.pcolormesh(xi, yi, zi.reshape(xi.shape), cmap=cmap)
-
         if greyblock:
-            axes.add_patch(mpatches.Polygon([[birth.min(), birth.min()], [death.max(), birth.min()], [death.max(), death.max()]], fill=True, color='lightgrey'))
+            axes.add_patch(
+                mpatches.Polygon(
+                    [[birth_min, birth_min], [death_max, birth_min], [death_max, death_max]],
+                    fill=True,
+                    color="lightgrey",
+                )
+            )
 
-        if legend:
+        if plot_success and legend:
             plt.colorbar(img, ax=axes)
 
         axes.set_xlabel("Birth", fontsize=fontsize)
@@ -521,7 +516,5 @@ def plot_persistence_density(
 
         return axes
 
-    except ImportError:
-        print(
-            "This function is not available, you may be missing matplotlib and/or scipy."
-        )
+    except ImportError as import_error:
+        warnings.warn(f"This function is not available.\nModuleNotFoundError: No module named '{import_error.name}'.")
diff --git a/src/python/gudhi/simplex_tree.pxd b/src/python/gudhi/simplex_tree.pxd
index 70311ead..4f229663 100644
--- a/src/python/gudhi/simplex_tree.pxd
+++ b/src/python/gudhi/simplex_tree.pxd
@@ -45,6 +45,7 @@ cdef extern from "Simplex_tree_interface.h" namespace "Gudhi":
 
     cdef cppclass Simplex_tree_interface_full_featured "Gudhi::Simplex_tree_interface<Gudhi::Simplex_tree_options_full_featured>":
         Simplex_tree_interface_full_featured() nogil
+        Simplex_tree_interface_full_featured(Simplex_tree_interface_full_featured&) nogil
         double simplex_filtration(vector[int] simplex) nogil
         void assign_simplex_filtration(vector[int] simplex, double filtration) nogil
         void initialize_filtration() nogil
@@ -75,6 +76,9 @@ cdef extern from "Simplex_tree_interface.h" namespace "Gudhi":
         Simplex_tree_skeleton_iterator get_skeleton_iterator_begin(int dimension) nogil
         Simplex_tree_skeleton_iterator get_skeleton_iterator_end(int dimension) nogil
         pair[Simplex_tree_boundary_iterator, Simplex_tree_boundary_iterator] get_boundary_iterators(vector[int] simplex) nogil except +
+        # Expansion with blockers
+        ctypedef bool (*blocker_func_t)(vector[int], void *user_data)
+        void expansion_with_blockers_callback(int dimension, blocker_func_t user_func, void *user_data)
 
 cdef extern from "Persistent_cohomology_interface.h" namespace "Gudhi":
     cdef cppclass Simplex_tree_persistence_interface "Gudhi::Persistent_cohomology_interface<Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_full_featured>>":
diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx
index 3d7c28b6..2c53a872 100644
--- a/src/python/gudhi/simplex_tree.pyx
+++ b/src/python/gudhi/simplex_tree.pyx
@@ -16,6 +16,9 @@ __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
 
+cdef bool callback(vector[int] simplex, void *blocker_func):
+    return (<object>blocker_func)(simplex)
+
 # SimplexTree python interface
 cdef class SimplexTree:
     """The simplex tree is an efficient and flexible data structure for
@@ -38,13 +41,29 @@ cdef class SimplexTree:
     cdef Simplex_tree_persistence_interface * pcohptr
 
     # Fake constructor that does nothing but documenting the constructor
-    def __init__(self):
+    def __init__(self, other = None):
         """SimplexTree constructor.
+
+        :param other: If `other` is `None` (default value), an empty `SimplexTree` is created.
+            If `other` is a `SimplexTree`, the `SimplexTree` is constructed from a deep copy of `other`.
+        :type other: SimplexTree (Optional)
+        :returns: An empty or a copy simplex tree.
+        :rtype: SimplexTree
+
+        :raises TypeError: In case `other` is neither `None`, nor a `SimplexTree`.
+        :note: If the `SimplexTree` is a copy, the persistence information is not copied. If you need it in the clone,
+            you have to call :func:`compute_persistence` on it even if you had already computed it in the original.
         """
 
     # The real cython constructor
-    def __cinit__(self):
-        self.thisptr = <intptr_t>(new Simplex_tree_interface_full_featured())
+    def __cinit__(self, other = None):
+        if other:
+            if isinstance(other, SimplexTree):
+                self.thisptr = _get_copy_intptr(other)
+            else:
+                raise TypeError("`other` argument requires to be of type `SimplexTree`, or `None`.")
+        else:
+            self.thisptr = <intptr_t>(new Simplex_tree_interface_full_featured())
 
     def __dealloc__(self):
         cdef Simplex_tree_interface_full_featured* ptr = self.get_ptr()
@@ -63,6 +82,21 @@ cdef class SimplexTree:
          """
         return self.pcohptr != NULL
 
+    def copy(self):
+        """ 
+        :returns: A simplex tree that is a deep copy of itself.
+        :rtype: SimplexTree
+
+        :note: The persistence information is not copied. If you need it in the clone, you have to call
+            :func:`compute_persistence` on it even if you had already computed it in the original.
+        """
+        stree = SimplexTree()
+        stree.thisptr = _get_copy_intptr(self)
+        return stree
+
+    def __deepcopy__(self):
+        return self.copy()
+
     def filtration(self, simplex):
         """This function returns the filtration value for a given N-simplex in
         this simplicial complex, or +infinity if it is not in the complex.
@@ -443,6 +477,27 @@ cdef class SimplexTree:
         persistence_result = self.pcohptr.get_persistence()
         return self.get_ptr().compute_extended_persistence_subdiagrams(persistence_result, min_persistence)
 
+    def expansion_with_blocker(self, max_dim, blocker_func):
+        """Expands the Simplex_tree containing only a graph. Simplices corresponding to cliques in the graph are added
+        incrementally, faces before cofaces, unless the simplex has dimension larger than `max_dim` or `blocker_func`
+        returns `True` for this simplex.
+
+        The function identifies a candidate simplex whose faces are all already in the complex, inserts it with a
+        filtration value corresponding to the maximum of the filtration values of the faces, then calls `blocker_func`
+        with this new simplex (represented as a list of int). If `blocker_func` returns `True`, the simplex is removed,
+        otherwise it is kept. The algorithm then proceeds with the next candidate.
+
+        .. warning::
+            Several candidates of the same dimension may be inserted simultaneously before calling `block_simplex`, so
+            if you examine the complex in `block_simplex`, you may hit a few simplices of the same dimension that have
+            not been vetted by `block_simplex` yet, or have already been rejected but not yet removed.
+
+        :param max_dim: Expansion maximal dimension value.
+        :type max_dim: int
+        :param blocker_func: Blocker oracle.
+        :type blocker_func: Callable[[List[int]], bool]
+        """
+        self.get_ptr().expansion_with_blockers_callback(max_dim, callback, <void*>blocker_func)
 
     def persistence(self, homology_coeff_field=11, min_persistence=0, persistence_dim_max = False):
         """This function computes and returns the persistence of the simplicial complex.
@@ -648,3 +703,6 @@ cdef class SimplexTree:
         :rtype: bool
         """
         return dereference(self.get_ptr()) == dereference(other.get_ptr())
+
+cdef intptr_t _get_copy_intptr(SimplexTree stree) nogil:
+    return <intptr_t>(new Simplex_tree_interface_full_featured(dereference(stree.get_ptr())))
diff --git a/src/python/include/Alpha_complex_interface.h b/src/python/include/Alpha_complex_interface.h
index 671af4a4..469b91ce 100644
--- a/src/python/include/Alpha_complex_interface.h
+++ b/src/python/include/Alpha_complex_interface.h
@@ -57,6 +57,16 @@ class Alpha_complex_interface {
       alpha_ptr_->create_simplex_tree(simplex_tree, max_alpha_square, default_filtration_value);
   }
 
+  static void set_float_relative_precision(double precision) {
+    // cf. Exact_alpha_complex_dD kernel type in Alpha_complex_factory.h
+    CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>::FT::set_relative_precision_of_to_double(precision);
+  }
+
+  static double get_float_relative_precision() {
+    // cf. Exact_alpha_complex_dD kernel type in Alpha_complex_factory.h
+    return CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>::FT::get_relative_precision_of_to_double();
+  }
+
  private:
   std::unique_ptr<Abstract_alpha_complex> alpha_ptr_;
 };
diff --git a/src/python/include/Simplex_tree_interface.h b/src/python/include/Simplex_tree_interface.h
index 4d8f8537..7f9b0067 100644
--- a/src/python/include/Simplex_tree_interface.h
+++ b/src/python/include/Simplex_tree_interface.h
@@ -40,6 +40,7 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
   using Complex_simplex_iterator = typename Base::Complex_simplex_iterator;
   using Extended_filtration_data = typename Base::Extended_filtration_data;
   using Boundary_simplex_iterator = typename Base::Boundary_simplex_iterator;
+  typedef bool (*blocker_func_t)(Simplex simplex, void *user_data);
 
  public:
 
@@ -189,6 +190,13 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
     return collapsed_stree_ptr;
   }
 
+  void expansion_with_blockers_callback(int dimension, blocker_func_t user_func, void *user_data) {
+    Base::expansion_with_blockers(dimension, [&](Simplex_handle sh){
+      Simplex simplex(Base::simplex_vertex_range(sh).begin(), Base::simplex_vertex_range(sh).end());
+      return user_func(simplex, user_data);
+    });
+  }
+
   // 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 f15284f3..f81e6137 100755
--- a/src/python/test/test_alpha_complex.py
+++ b/src/python/test/test_alpha_complex.py
@@ -286,3 +286,30 @@ def _weighted_doc_example(precision):
 def test_weighted_doc_example():
     for precision in ['fast', 'safe', 'exact']:
         _weighted_doc_example(precision)
+
+def test_float_relative_precision():
+    assert AlphaComplex.get_float_relative_precision() == 1e-5
+    # Must be > 0.
+    with pytest.raises(ValueError):
+        AlphaComplex.set_float_relative_precision(0.)
+    # Must be < 1.
+    with pytest.raises(ValueError):
+        AlphaComplex.set_float_relative_precision(1.)
+
+    points = [[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]]
+    st = AlphaComplex(points=points).create_simplex_tree()
+    filtrations = list(st.get_filtration())
+
+    # Get a better precision
+    AlphaComplex.set_float_relative_precision(1e-15)
+    assert AlphaComplex.get_float_relative_precision() == 1e-15
+
+    st = AlphaComplex(points=points).create_simplex_tree()
+    filtrations_better_resolution = list(st.get_filtration())
+
+    assert len(filtrations) == len(filtrations_better_resolution)
+    for idx in range(len(filtrations)):
+        # check simplex is the same
+        assert filtrations[idx][0] == filtrations_better_resolution[idx][0]
+        # check filtration is about the same with a relative precision of the worst case
+        assert filtrations[idx][1] == pytest.approx(filtrations_better_resolution[idx][1], rel=1e-5)
diff --git a/src/python/test/test_persistence_graphical_tools.py b/src/python/test/test_persistence_graphical_tools.py
new file mode 100644
index 00000000..c19836b7
--- /dev/null
+++ b/src/python/test/test_persistence_graphical_tools.py
@@ -0,0 +1,121 @@
+""" 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) 2021 Inria
+
+    Modification(s):
+      - YYYY/MM Author: Description of the modification
+"""
+
+import gudhi as gd
+import numpy as np
+import matplotlib as plt
+import pytest
+
+
+def test_array_handler():
+    diags = np.array([[1, 2], [3, 4], [5, 6]], float)
+    arr_diags = gd.persistence_graphical_tools._array_handler(diags)
+    for idx in range(len(diags)):
+        assert arr_diags[idx][0] == 0
+        np.testing.assert_array_equal(arr_diags[idx][1], diags[idx])
+
+    diags = [(1.0, 2.0), (3.0, 4.0), (5.0, 6.0)]
+    arr_diags = gd.persistence_graphical_tools._array_handler(diags)
+    for idx in range(len(diags)):
+        assert arr_diags[idx][0] == 0
+        assert arr_diags[idx][1] == diags[idx]
+
+    diags = [(0, (1.0, 2.0)), (0, (3.0, 4.0)), (0, (5.0, 6.0))]
+    assert gd.persistence_graphical_tools._array_handler(diags) == diags
+
+
+def test_min_birth_max_death():
+    diags = [
+        (0, (0.0, float("inf"))),
+        (0, (0.0983494, float("inf"))),
+        (0, (0.0, 0.122545)),
+        (0, (0.0, 0.12047)),
+        (0, (0.0, 0.118398)),
+        (0, (0.118398, 1.0)),
+        (0, (0.0, 0.117908)),
+        (0, (0.0, 0.112307)),
+        (0, (0.0, 0.107535)),
+        (0, (0.0, 0.106382)),
+    ]
+    assert gd.persistence_graphical_tools.__min_birth_max_death(diags) == (0.0, 1.0)
+    assert gd.persistence_graphical_tools.__min_birth_max_death(diags, band=4.0) == (0.0, 5.0)
+
+
+def test_limit_min_birth_max_death():
+    diags = [
+        (0, (2.0, float("inf"))),
+        (0, (2.0, float("inf"))),
+    ]
+    assert gd.persistence_graphical_tools.__min_birth_max_death(diags) == (2.0, 3.0)
+    assert gd.persistence_graphical_tools.__min_birth_max_death(diags, band=4.0) == (2.0, 6.0)
+
+
+def test_limit_to_max_intervals():
+    diags = [
+        (0, (0.0, float("inf"))),
+        (0, (0.0983494, float("inf"))),
+        (0, (0.0, 0.122545)),
+        (0, (0.0, 0.12047)),
+        (0, (0.0, 0.118398)),
+        (0, (0.118398, 1.0)),
+        (0, (0.0, 0.117908)),
+        (0, (0.0, 0.112307)),
+        (0, (0.0, 0.107535)),
+        (0, (0.0, 0.106382)),
+    ]
+    # check no warnings if max_intervals equals to the diagrams number
+    with pytest.warns(None) as record:
+        truncated_diags = gd.persistence_graphical_tools._limit_to_max_intervals(
+            diags, 10, key=lambda life_time: life_time[1][1] - life_time[1][0]
+        )
+        # check diagrams are not sorted
+        assert truncated_diags == diags
+    assert len(record) == 0
+
+    # check warning if max_intervals lower than the diagrams number
+    with pytest.warns(UserWarning) as record:
+        truncated_diags = gd.persistence_graphical_tools._limit_to_max_intervals(
+            diags, 5, key=lambda life_time: life_time[1][1] - life_time[1][0]
+        )
+        # check diagrams are truncated and sorted by life time
+        assert truncated_diags == [
+            (0, (0.0, float("inf"))),
+            (0, (0.0983494, float("inf"))),
+            (0, (0.118398, 1.0)),
+            (0, (0.0, 0.122545)),
+            (0, (0.0, 0.12047)),
+        ]
+    assert len(record) == 1
+
+
+def _limit_plot_persistence(function):
+    pplot = function(persistence=[])
+    assert isinstance(pplot, plt.axes.SubplotBase)
+    pplot = function(persistence=[], legend=True)
+    assert isinstance(pplot, plt.axes.SubplotBase)
+    pplot = function(persistence=[(0, float("inf"))])
+    assert isinstance(pplot, plt.axes.SubplotBase)
+    pplot = function(persistence=[(0, float("inf"))], legend=True)
+    assert isinstance(pplot, plt.axes.SubplotBase)
+
+
+def test_limit_plot_persistence():
+    for function in [gd.plot_persistence_barcode, gd.plot_persistence_diagram, gd.plot_persistence_density]:
+        _limit_plot_persistence(function)
+
+
+def _non_existing_persistence_file(function):
+    with pytest.raises(FileNotFoundError):
+        function(persistence_file="pouetpouettralala.toubiloubabdou")
+
+
+def test_non_existing_persistence_file():
+    for function in [gd.plot_persistence_barcode, gd.plot_persistence_diagram, gd.plot_persistence_density]:
+        _non_existing_persistence_file(function)
diff --git a/src/python/test/test_simplex_tree.py b/src/python/test/test_simplex_tree.py
index f130cf1f..688f4fd6 100755
--- a/src/python/test/test_simplex_tree.py
+++ b/src/python/test/test_simplex_tree.py
@@ -454,3 +454,104 @@ def test_equality_operator():
 
     st2.insert([1,2,3], 4.)
     assert st1 == st2
+
+def test_simplex_tree_deep_copy():
+    st = SimplexTree()
+    st.insert([1, 2, 3], 0.)
+    # compute persistence only on the original
+    st.compute_persistence()
+
+    st_copy = st.copy()
+    assert st_copy == st
+    st_filt_list = list(st.get_filtration())
+
+    # check persistence is not copied
+    assert st.__is_persistence_defined() == True
+    assert st_copy.__is_persistence_defined() == False
+
+    # remove something in the copy and check the copy is included in the original
+    st_copy.remove_maximal_simplex([1, 2, 3])
+    a_filt_list = list(st_copy.get_filtration())
+    assert len(a_filt_list) < len(st_filt_list)
+
+    for a_splx in a_filt_list:
+        assert a_splx in st_filt_list
+    
+    # test double free
+    del st
+    del st_copy
+
+def test_simplex_tree_deep_copy_constructor():
+    st = SimplexTree()
+    st.insert([1, 2, 3], 0.)
+    # compute persistence only on the original
+    st.compute_persistence()
+
+    st_copy = SimplexTree(st)
+    assert st_copy == st
+    st_filt_list = list(st.get_filtration())
+
+    # check persistence is not copied
+    assert st.__is_persistence_defined() == True
+    assert st_copy.__is_persistence_defined() == False
+
+    # remove something in the copy and check the copy is included in the original
+    st_copy.remove_maximal_simplex([1, 2, 3])
+    a_filt_list = list(st_copy.get_filtration())
+    assert len(a_filt_list) < len(st_filt_list)
+
+    for a_splx in a_filt_list:
+        assert a_splx in st_filt_list
+    
+    # test double free
+    del st
+    del st_copy
+
+def test_simplex_tree_constructor_exception():
+    with pytest.raises(TypeError):
+        st = SimplexTree(other = "Construction from a string shall raise an exception")
+
+def test_expansion_with_blocker():
+    st=SimplexTree()
+    st.insert([0,1],0)
+    st.insert([0,2],1)
+    st.insert([0,3],2)
+    st.insert([1,2],3)
+    st.insert([1,3],4)
+    st.insert([2,3],5)
+    st.insert([2,4],6)
+    st.insert([3,6],7)
+    st.insert([4,5],8)
+    st.insert([4,6],9)
+    st.insert([5,6],10)
+    st.insert([6],10)
+
+    def blocker(simplex):
+        try:
+            # Block all simplices that countains vertex 6
+            simplex.index(6)
+            print(simplex, ' is blocked')
+            return True
+        except ValueError:
+            print(simplex, ' is accepted')
+            st.assign_filtration(simplex, st.filtration(simplex) + 1.)
+            return False
+
+    st.expansion_with_blocker(2, blocker)
+    assert st.num_simplices() == 22
+    assert st.dimension() == 2
+    assert st.find([4,5,6]) == False
+    assert st.filtration([0,1,2]) == 4.
+    assert st.filtration([0,1,3]) == 5.
+    assert st.filtration([0,2,3]) == 6.
+    assert st.filtration([1,2,3]) == 6.
+
+    st.expansion_with_blocker(3, blocker)
+    assert st.num_simplices() == 23
+    assert st.dimension() == 3
+    assert st.find([4,5,6]) == False
+    assert st.filtration([0,1,2]) == 4.
+    assert st.filtration([0,1,3]) == 5.
+    assert st.filtration([0,2,3]) == 6.
+    assert st.filtration([1,2,3]) == 6.
+    assert st.filtration([0,1,2,3]) == 7.