update from upstream/master and merge CMakeLists

20 files changed, 341 insertions, 229 deletions

diff --git a/src/python/gudhi/__init__.py.in b/src/python/gudhi/__init__.py.in
index 0c462b02..79e12fbc 100644
--- a/src/python/gudhi/__init__.py.in
+++ b/src/python/gudhi/__init__.py.in
@@ -1,5 +1,3 @@
-from importlib import import_module
-
 # 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
@@ -9,6 +7,9 @@ from importlib import import_module
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from importlib import import_module
+from sys import exc_info
+
 __author__ = "GUDHI Editorial Board"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "https://gudhi.inria.fr/licensing/"
@@ -17,9 +18,6 @@ __version__ = "@GUDHI_VERSION@"
 __root_source_dir__ = "@CMAKE_SOURCE_DIR@"
 __debug_info__ = @GUDHI_PYTHON_DEBUG_INFO@
 
-from sys import exc_info
-from importlib import import_module
-
 __all__ = [@GUDHI_PYTHON_MODULES@ @GUDHI_PYTHON_MODULES_EXTRA@]
 
 __available_modules = ''
diff --git a/src/python/gudhi/alpha_complex.pyx b/src/python/gudhi/alpha_complex.pyx
index 8f2c98d5..fff3e920 100644
--- a/src/python/gudhi/alpha_complex.pyx
+++ b/src/python/gudhi/alpha_complex.pyx
@@ -1,3 +1,12 @@
+# 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
+
 from cython cimport numeric
 from libcpp.vector cimport vector
 from libcpp.utility cimport pair
@@ -9,26 +18,17 @@ import os
 from gudhi.simplex_tree cimport *
 from gudhi.simplex_tree import SimplexTree
 
-# 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) 2016 Inria"
 __license__ = "GPL v3"
 
 cdef extern from "Alpha_complex_interface.h" namespace "Gudhi":
     cdef cppclass Alpha_complex_interface "Gudhi::alpha_complex::Alpha_complex_interface":
-        Alpha_complex_interface(vector[vector[double]] points)
+        Alpha_complex_interface(vector[vector[double]] points) except +
         # bool from_file is a workaround for cython to find the correct signature
-        Alpha_complex_interface(string off_file, bool from_file)
-        vector[double] get_point(int vertex)
-        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square)
+        Alpha_complex_interface(string off_file, bool from_file) except +
+        vector[double] get_point(int vertex) except +
+        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square) except +
 
 # AlphaComplex python interface
 cdef class AlphaComplex:
@@ -66,10 +66,10 @@ cdef class AlphaComplex:
         """
 
     # The real cython constructor
-    def __cinit__(self, points=None, off_file=''):
+    def __cinit__(self, points = None, off_file = ''):
         if off_file:
             if os.path.isfile(off_file):
-                self.thisptr = new Alpha_complex_interface(str.encode(off_file), True)
+                self.thisptr = new Alpha_complex_interface(off_file.encode('utf-8'), True)
             else:
                 print("file " + off_file + " not found.")
         else:
@@ -96,10 +96,9 @@ cdef class AlphaComplex:
         :rtype: list of float
         :returns: the point.
         """
-        cdef vector[double] point = self.thisptr.get_point(vertex)
-        return point
+        return self.thisptr.get_point(vertex)
 
-    def create_simplex_tree(self, max_alpha_square=float('inf')):
+    def create_simplex_tree(self, max_alpha_square = float('inf')):
         """
         :param max_alpha_square: The maximum alpha square threshold the
             simplices shall not exceed. Default is set to infinity, and
diff --git a/src/python/gudhi/bottleneck.pyx b/src/python/gudhi/bottleneck.pyx
index c2361024..af011e88 100644
--- a/src/python/gudhi/bottleneck.pyx
+++ b/src/python/gudhi/bottleneck.pyx
@@ -1,8 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.utility cimport pair
-import os
-
 # 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
@@ -12,6 +7,11 @@ import os
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.utility cimport pair
+import os
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "GPL v3"
diff --git a/src/python/gudhi/cubical_complex.pyx b/src/python/gudhi/cubical_complex.pyx
index 011c407c..cbeda014 100644
--- a/src/python/gudhi/cubical_complex.pyx
+++ b/src/python/gudhi/cubical_complex.pyx
@@ -1,12 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.utility cimport pair
-from libcpp.string cimport string
-from libcpp cimport bool
-import os
-
-from numpy import array as np_array
-
 # 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
@@ -16,6 +7,15 @@ from numpy import array as np_array
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.utility cimport pair
+from libcpp.string cimport string
+from libcpp cimport bool
+import os
+
+import numpy as np
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
@@ -47,7 +47,7 @@ cdef class CubicalComplex:
 
     # Fake constructor that does nothing but documenting the constructor
     def __init__(self, dimensions=None, top_dimensional_cells=None,
-                  perseus_file=''):
+                 perseus_file=''):
         """CubicalComplex constructor from dimensions and
         top_dimensional_cells or from a Perseus-style file name.
 
@@ -58,6 +58,12 @@ cdef class CubicalComplex:
 
         Or
 
+        :param top_dimensional_cells: A multidimensional array of cells
+            filtration values.
+        :type top_dimensional_cells: anything convertible to a numpy ndarray
+
+        Or
+
         :param perseus_file: A Perseus-style file name.
         :type perseus_file: string
         """
@@ -65,11 +71,21 @@ cdef class CubicalComplex:
     # The real cython constructor
     def __cinit__(self, dimensions=None, top_dimensional_cells=None,
                   perseus_file=''):
-        if (dimensions is not None) and (top_dimensional_cells is not None) and (perseus_file == ''):
+        if ((dimensions is not None) and (top_dimensional_cells is not None)
+            and (perseus_file == '')):
+            self.thisptr = new Bitmap_cubical_complex_base_interface(dimensions, top_dimensional_cells)
+        elif ((dimensions is None) and (top_dimensional_cells is not None)
+            and (perseus_file == '')):
+            top_dimensional_cells = np.array(top_dimensional_cells,
+                                             copy = False,
+                                             order = 'F')
+            dimensions = top_dimensional_cells.shape
+            top_dimensional_cells = top_dimensional_cells.ravel(order='F')
             self.thisptr = new Bitmap_cubical_complex_base_interface(dimensions, top_dimensional_cells)
-        elif (dimensions is None) and (top_dimensional_cells is None) and (perseus_file != ''):
+        elif ((dimensions is None) and (top_dimensional_cells is None)
+            and (perseus_file != '')):
             if os.path.isfile(perseus_file):
-                self.thisptr = new Bitmap_cubical_complex_base_interface(str.encode(perseus_file))
+                self.thisptr = new Bitmap_cubical_complex_base_interface(perseus_file.encode('utf-8'))
             else:
                 print("file " + perseus_file + " not found.")
         else:
@@ -184,4 +200,4 @@ cdef class CubicalComplex:
         else:
             print("intervals_in_dim function requires persistence function"
                   " to be launched first.")
-        return np_array(intervals_result)
+        return np.array(intervals_result)
diff --git a/src/python/gudhi/euclidean_strong_witness_complex.pyx b/src/python/gudhi/euclidean_strong_witness_complex.pyx
index e3f451f0..aca6084e 100644
--- a/src/python/gudhi/euclidean_strong_witness_complex.pyx
+++ b/src/python/gudhi/euclidean_strong_witness_complex.pyx
@@ -1,11 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.utility cimport pair
-from libc.stdint cimport intptr_t
-
-from gudhi.simplex_tree cimport *
-from gudhi.simplex_tree import SimplexTree
-
 # 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
@@ -15,6 +7,14 @@ from gudhi.simplex_tree import SimplexTree
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.utility cimport pair
+from libc.stdint cimport intptr_t
+
+from gudhi.simplex_tree cimport *
+from gudhi.simplex_tree import SimplexTree
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "GPL v3"
@@ -22,9 +22,9 @@ __license__ = "GPL v3"
 cdef extern from "Euclidean_strong_witness_complex_interface.h" namespace "Gudhi":
     cdef cppclass Euclidean_strong_witness_complex_interface "Gudhi::witness_complex::Euclidean_strong_witness_complex_interface":
         Euclidean_strong_witness_complex_interface(vector[vector[double]] landmarks, vector[vector[double]] witnesses)
-        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square)
+        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square) except +
         void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square,
-            unsigned limit_dimension)
+            unsigned limit_dimension) except +
         vector[double] get_point(unsigned vertex)
 
 # EuclideanStrongWitnessComplex python interface
diff --git a/src/python/gudhi/euclidean_witness_complex.pyx b/src/python/gudhi/euclidean_witness_complex.pyx
index 84a8ea1a..fb0c2201 100644
--- a/src/python/gudhi/euclidean_witness_complex.pyx
+++ b/src/python/gudhi/euclidean_witness_complex.pyx
@@ -1,11 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.utility cimport pair
-from libc.stdint cimport intptr_t
-
-from gudhi.simplex_tree cimport *
-from gudhi.simplex_tree import SimplexTree
-
 # 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
@@ -15,6 +7,14 @@ from gudhi.simplex_tree import SimplexTree
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.utility cimport pair
+from libc.stdint cimport intptr_t
+
+from gudhi.simplex_tree cimport *
+from gudhi.simplex_tree import SimplexTree
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "GPL v3"
@@ -22,9 +22,9 @@ __license__ = "GPL v3"
 cdef extern from "Euclidean_witness_complex_interface.h" namespace "Gudhi":
     cdef cppclass Euclidean_witness_complex_interface "Gudhi::witness_complex::Euclidean_witness_complex_interface":
         Euclidean_witness_complex_interface(vector[vector[double]] landmarks, vector[vector[double]] witnesses)
-        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square)
+        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square) except +
         void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square,
-            unsigned limit_dimension)
+            unsigned limit_dimension) except +
         vector[double] get_point(unsigned vertex)
 
 # EuclideanWitnessComplex python interface
diff --git a/src/python/gudhi/hera.cc b/src/python/gudhi/hera.cc
new file mode 100644
index 00000000..0d562b4c
--- /dev/null
+++ b/src/python/gudhi/hera.cc
@@ -0,0 +1,71 @@
+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Marc Glisse
+ *
+ *    Copyright (C) 2020 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#include <pybind11/pybind11.h>
+#include <pybind11/numpy.h>
+
+#include <boost/range/iterator_range.hpp>
+
+#include <wasserstein.h> // Hera
+
+#include <array>
+
+namespace py = pybind11;
+typedef py::array_t<double, py::array::c_style | py::array::forcecast> Dgm;
+
+double wasserstein_distance(
+    Dgm d1, Dgm d2,
+    double wasserstein_power, double internal_p,
+    double delta)
+{
+  py::buffer_info buf1 = d1.request();
+  py::buffer_info buf2 = d2.request();
+  // shape (n,2) or (0) for empty
+  if((buf1.ndim!=2 || buf1.shape[1]!=2) && (buf1.ndim!=1 || buf1.shape[0]!=0))
+    throw std::runtime_error("Diagram 1 must be an array of size n x 2");
+  if((buf2.ndim!=2 || buf2.shape[1]!=2) && (buf2.ndim!=1 || buf2.shape[0]!=0))
+    throw std::runtime_error("Diagram 2 must be an array of size n x 2");
+  typedef std::array<double, 2> Point;
+  auto p1 = (Point*)buf1.ptr;
+  auto p2 = (Point*)buf2.ptr;
+  auto diag1 = boost::make_iterator_range(p1, p1+buf1.shape[0]);
+  auto diag2 = boost::make_iterator_range(p2, p2+buf2.shape[0]);
+
+  hera::AuctionParams<double> params;
+  params.wasserstein_power = wasserstein_power;
+  // hera encodes infinity as -1...
+  if(std::isinf(internal_p)) internal_p = hera::get_infinity<double>();
+  params.internal_p = internal_p;
+  params.delta = delta;
+  // The extra parameters are purposedly not exposed for now.
+  return hera::wasserstein_dist(diag1, diag2, params);
+}
+
+PYBIND11_MODULE(hera, m) {
+      m.def("wasserstein_distance", &wasserstein_distance,
+          py::arg("X"), py::arg("Y"),
+          py::arg("order") = 1,
+          py::arg("internal_p") = std::numeric_limits<double>::infinity(),
+          py::arg("delta") = .01,
+          R"pbdoc(
+        Compute the Wasserstein distance between two diagrams.
+        Points at infinity are supported.
+
+        Parameters:
+            X (n x 2 numpy array): First diagram
+            Y (n x 2 numpy array): Second diagram
+            order (float): Wasserstein exponent W_q
+            internal_p (float): Internal Minkowski norm L^p in R^2
+            delta (float): Relative error 1+delta
+
+        Returns:
+            float: Approximate Wasserstein distance W_q(X,Y)
+    )pbdoc");
+}
diff --git a/src/python/gudhi/nerve_gic.pyx b/src/python/gudhi/nerve_gic.pyx
index acb78564..382e71c5 100644
--- a/src/python/gudhi/nerve_gic.pyx
+++ b/src/python/gudhi/nerve_gic.pyx
@@ -1,3 +1,12 @@
+# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+# Author(s):       Vincent Rouvreau
+#
+# Copyright (C) 2018 Inria
+#
+# Modification(s):
+#   - YYYY/MM Author: Description of the modification
+
 from cython cimport numeric
 from libcpp.vector cimport vector
 from libcpp.utility cimport pair
@@ -9,15 +18,6 @@ from libc.stdint cimport intptr_t
 from gudhi.simplex_tree cimport *
 from gudhi.simplex_tree import SimplexTree
 
-# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
-# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
-# Author(s):       Vincent Rouvreau
-#
-# Copyright (C) 2018 Inria
-#
-# Modification(s):
-#   - YYYY/MM Author: Description of the modification
-
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2018 Inria"
 __license__ = "GPL v3"
@@ -180,7 +180,7 @@ cdef class CoverComplex:
         :returns: Read file status.
         """
         if os.path.isfile(off_file):
-            return self.thisptr.read_point_cloud(str.encode(off_file))
+            return self.thisptr.read_point_cloud(off_file.encode('utf-8'))
         else:
             print("file " + off_file + " not found.")
             return False
@@ -212,7 +212,7 @@ cdef class CoverComplex:
         :type color_file_name: string
         """
         if os.path.isfile(color_file_name):
-            self.thisptr.set_color_from_file(str.encode(color_file_name))
+            self.thisptr.set_color_from_file(color_file_name.encode('utf-8'))
         else:
             print("file " + color_file_name + " not found.")
 
@@ -233,7 +233,7 @@ cdef class CoverComplex:
         :type cover_file_name: string
         """
         if os.path.isfile(cover_file_name):
-            self.thisptr.set_cover_from_file(str.encode(cover_file_name))
+            self.thisptr.set_cover_from_file(cover_file_name.encode('utf-8'))
         else:
             print("file " + cover_file_name + " not found.")
 
@@ -266,7 +266,7 @@ cdef class CoverComplex:
         :type func_file_name: string
         """
         if os.path.isfile(func_file_name):
-            self.thisptr.set_function_from_file(str.encode(func_file_name))
+            self.thisptr.set_function_from_file(func_file_name.encode('utf-8'))
         else:
             print("file " + func_file_name + " not found.")
 
@@ -307,7 +307,7 @@ cdef class CoverComplex:
         :type graph_file_name: string
         """
         if os.path.isfile(graph_file_name):
-            self.thisptr.set_graph_from_file(str.encode(graph_file_name))
+            self.thisptr.set_graph_from_file(graph_file_name.encode('utf-8'))
         else:
             print("file " + graph_file_name + " not found.")
 
@@ -368,7 +368,7 @@ cdef class CoverComplex:
         :param type: either "GIC" or "Nerve".
         :type type: string
         """
-        self.thisptr.set_type(str.encode(type))
+        self.thisptr.set_type(type.encode('utf-8'))
 
     def set_verbose(self, verbose):
         """Specifies whether the program should display information or not.
diff --git a/src/python/gudhi/off_reader.pyx b/src/python/gudhi/off_reader.pyx
index 225e981c..7e6d9d80 100644
--- a/src/python/gudhi/off_reader.pyx
+++ b/src/python/gudhi/off_reader.pyx
@@ -1,8 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.string cimport string
-import os
-
 # 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
@@ -12,6 +7,11 @@ import os
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.string cimport string
+import os
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
@@ -19,18 +19,18 @@ __license__ = "MIT"
 cdef extern from "Off_reader_interface.h" namespace "Gudhi":
     vector[vector[double]] read_points_from_OFF_file(string off_file)
 
-def read_off(off_file=''):
+def read_points_from_off_file(off_file=''):
     """Read points from OFF file.
 
     :param off_file: An OFF file style name.
     :type off_file: string
 
     :returns:  The point set.
-    :rtype: vector[vector[double]]
+    :rtype: List[List[float]]
     """
     if off_file:
         if os.path.isfile(off_file):
-            return read_points_from_OFF_file(str.encode(off_file))
+            return read_points_from_OFF_file(off_file.encode('utf-8'))
         else:
             print("file " + off_file + " not found.")
             return []
diff --git a/src/python/gudhi/periodic_cubical_complex.pyx b/src/python/gudhi/periodic_cubical_complex.pyx
index c89055db..37f76201 100644
--- a/src/python/gudhi/periodic_cubical_complex.pyx
+++ b/src/python/gudhi/periodic_cubical_complex.pyx
@@ -1,12 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.utility cimport pair
-from libcpp.string cimport string
-from libcpp cimport bool
-import os
-
-from numpy import array as np_array
-
 # 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
@@ -16,6 +7,15 @@ from numpy import array as np_array
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.utility cimport pair
+from libcpp.string cimport string
+from libcpp cimport bool
+import os
+
+import numpy as np
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
@@ -47,7 +47,7 @@ cdef class PeriodicCubicalComplex:
 
     # Fake constructor that does nothing but documenting the constructor
     def __init__(self, dimensions=None, top_dimensional_cells=None,
-                  periodic_dimensions=None, perseus_file=''):
+                 periodic_dimensions=None, perseus_file=''):
         """PeriodicCubicalComplex constructor from dimensions and
         top_dimensional_cells or from a Perseus-style file name.
 
@@ -60,6 +60,14 @@ cdef class PeriodicCubicalComplex:
 
         Or
 
+        :param top_dimensional_cells: A multidimensional array of cells
+            filtration values.
+        :type top_dimensional_cells: anything convertible to a numpy ndarray
+        :param periodic_dimensions: A list of top dimensional cells periodicity value.
+        :type periodic_dimensions: list of boolean
+
+        Or
+
         :param perseus_file: A Perseus-style file name.
         :type perseus_file: string
         """
@@ -67,16 +75,32 @@ cdef class PeriodicCubicalComplex:
     # The real cython constructor
     def __cinit__(self, dimensions=None, top_dimensional_cells=None,
                   periodic_dimensions=None, perseus_file=''):
-        if (dimensions is not None) and (top_dimensional_cells is not None) and (periodic_dimensions is not None) and (perseus_file == ''):
-            self.thisptr = new Periodic_cubical_complex_base_interface(dimensions, top_dimensional_cells, periodic_dimensions)
-        elif (dimensions is None) and (top_dimensional_cells is None) and (periodic_dimensions is None) and (perseus_file != ''):
+        if ((dimensions is not None) and (top_dimensional_cells is not None)
+            and (periodic_dimensions is not None) and (perseus_file == '')):
+            self.thisptr = new Periodic_cubical_complex_base_interface(dimensions,
+                                                                       top_dimensional_cells,
+                                                                       periodic_dimensions)
+        elif ((dimensions is None) and (top_dimensional_cells is not None)
+            and (periodic_dimensions is not None) and (perseus_file == '')):
+            top_dimensional_cells = np.array(top_dimensional_cells,
+                                             copy = False,
+                                             order = 'F')
+            dimensions = top_dimensional_cells.shape
+            top_dimensional_cells = top_dimensional_cells.ravel(order='F')
+            self.thisptr = new Periodic_cubical_complex_base_interface(dimensions,
+                                                                       top_dimensional_cells,
+                                                                       periodic_dimensions)
+        elif ((dimensions is None) and (top_dimensional_cells is None)
+            and (periodic_dimensions is None) and (perseus_file != '')):
             if os.path.isfile(perseus_file):
-                self.thisptr = new Periodic_cubical_complex_base_interface(str.encode(perseus_file))
+                self.thisptr = new Periodic_cubical_complex_base_interface(perseus_file.encode('utf-8'))
             else:
                 print("file " + perseus_file + " not found.")
         else:
-            print("CubicalComplex can be constructed from dimensions and "
-              "top_dimensional_cells or from a Perseus-style file name.")
+            print("CubicalComplex can be constructed from dimensions, "
+              "top_dimensional_cells and periodic_dimensions, or from "
+              "top_dimensional_cells and periodic_dimensions or from "
+              "a Perseus-style file name.")
 
     def __dealloc__(self):
         if self.thisptr != NULL:
@@ -186,4 +210,4 @@ cdef class PeriodicCubicalComplex:
         else:
             print("intervals_in_dim function requires persistence function"
                   " to be launched first.")
-        return np_array(intervals_result)
+        return np.array(intervals_result)
diff --git a/src/python/gudhi/persistence_graphical_tools.py b/src/python/gudhi/persistence_graphical_tools.py
index 7d232c85..246280de 100644
--- a/src/python/gudhi/persistence_graphical_tools.py
+++ b/src/python/gudhi/persistence_graphical_tools.py
@@ -1,10 +1,3 @@
-from os import path
-from math import isfinite
-import numpy as np
-
-from gudhi.reader_utils import read_persistence_intervals_in_dimension
-from gudhi.reader_utils import read_persistence_intervals_grouped_by_dimension
-
 # 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, Bertrand Michel
@@ -14,6 +7,13 @@ from gudhi.reader_utils import read_persistence_intervals_grouped_by_dimension
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from os import path
+from math import isfinite
+import numpy as np
+
+from gudhi.reader_utils import read_persistence_intervals_in_dimension
+from gudhi.reader_utils import read_persistence_intervals_grouped_by_dimension
+
 __author__ = "Vincent Rouvreau, Bertrand Michel"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
diff --git a/src/python/gudhi/reader_utils.pyx b/src/python/gudhi/reader_utils.pyx
index 6994c4f9..fe1c3a2e 100644
--- a/src/python/gudhi/reader_utils.pyx
+++ b/src/python/gudhi/reader_utils.pyx
@@ -1,12 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.string cimport string
-from libcpp.map cimport map
-from libcpp.pair cimport pair
-
-from os import path
-from numpy import array as np_array
-
 # 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
@@ -16,6 +7,15 @@ from numpy import array as np_array
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.string cimport string
+from libcpp.map cimport map
+from libcpp.pair cimport pair
+
+from os import path
+from numpy import array as np_array
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2017 Inria"
 __license__ = "MIT"
@@ -34,30 +34,30 @@ def read_lower_triangular_matrix_from_csv_file(csv_file='', separator=';'):
     :type separator: char
 
     :returns:  The lower triangular matrix.
-    :rtype: vector[vector[double]]
+    :rtype: List[List[float]]
     """
     if csv_file:
         if path.isfile(csv_file):
-            return read_matrix_from_csv_file(str.encode(csv_file), ord(separator[0]))
+            return read_matrix_from_csv_file(csv_file.encode('utf-8'), ord(separator[0]))
     print("file " + csv_file + " not set or not found.")
     return []
 
 def read_persistence_intervals_grouped_by_dimension(persistence_file=''):
     """Reads a file containing persistence intervals.
     Each line might contain 2, 3 or 4 values: [[field] dimension] birth death
-    The return value is an `map[dim, vector[pair[birth, death]]]`
-    where `dim` is an `int`, `birth` a `double`, and `death` a `double`.
+    The return value is a `dict(dim, list(tuple(birth, death)))`
+    where `dim` is an `int`, `birth` a `float`, and `death` a `float`.
     Note: the function does not check that birth <= death.
 
     :param persistence_file: A persistence file style name.
     :type persistence_file: string
 
     :returns:  The persistence pairs grouped by dimension.
-    :rtype: map[int, vector[pair[double, double]]]
+    :rtype: Dict[int, List[Tuple[float, float]]]
     """
     if persistence_file:
         if path.isfile(persistence_file):
-            return read_pers_intervals_grouped_by_dimension(str.encode(persistence_file))
+            return read_pers_intervals_grouped_by_dimension(persistence_file.encode('utf-8'))
     print("file " + persistence_file + " not set or not found.")
     return []
 
@@ -80,7 +80,7 @@ def read_persistence_intervals_in_dimension(persistence_file='', only_this_dim=-
     """
     if persistence_file:
         if path.isfile(persistence_file):
-            return np_array(read_pers_intervals_in_dimension(str.encode(
-                persistence_file), only_this_dim))
+            return np_array(read_pers_intervals_in_dimension(persistence_file.encode(
+                'utf-8'), only_this_dim))
     print("file " + persistence_file + " not set or not found.")
     return []
diff --git a/src/python/gudhi/rips_complex.pyx b/src/python/gudhi/rips_complex.pyx
index cbbbab0d..deb8057a 100644
--- a/src/python/gudhi/rips_complex.pyx
+++ b/src/python/gudhi/rips_complex.pyx
@@ -1,3 +1,12 @@
+# 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
+
 from cython cimport numeric
 from libcpp.vector cimport vector
 from libcpp.utility cimport pair
@@ -8,15 +17,6 @@ from libc.stdint cimport intptr_t
 from gudhi.simplex_tree cimport *
 from gudhi.simplex_tree import SimplexTree
 
-# 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) 2016 Inria"
 __license__ = "MIT"
@@ -28,7 +28,7 @@ cdef extern from "Rips_complex_interface.h" namespace "Gudhi":
         void init_matrix(vector[vector[double]] values, double threshold)
         void init_points_sparse(vector[vector[double]] values, double threshold, double sparse)
         void init_matrix_sparse(vector[vector[double]] values, double threshold, double sparse)
-        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, int dim_max)
+        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, int dim_max) except +
 
 # RipsComplex python interface
 cdef class RipsComplex:
diff --git a/src/python/gudhi/simplex_tree.pxd b/src/python/gudhi/simplex_tree.pxd
index 5f86cfe2..96d14079 100644
--- a/src/python/gudhi/simplex_tree.pxd
+++ b/src/python/gudhi/simplex_tree.pxd
@@ -1,19 +1,18 @@
+# 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
+
 from cython cimport numeric
 from libcpp.vector cimport vector
 from libcpp.utility cimport pair
 from libcpp cimport bool
 from libcpp.string cimport string
 
-""" 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) 2016 Inria"
 __license__ = "MIT"
@@ -40,7 +39,7 @@ cdef extern from "Simplex_tree_interface.h" namespace "Gudhi":
         vector[pair[vector[int], double]] get_star(vector[int] simplex)
         vector[pair[vector[int], double]] get_cofaces(vector[int] simplex,
                                                           int dimension)
-        void expansion(int max_dim)
+        void expansion(int max_dim) except +
         void remove_maximal_simplex(vector[int] simplex)
         bool prune_above_filtration(double filtration)
         bool make_filtration_non_decreasing()
diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx
index 4a3cd9bc..b18627c4 100644
--- a/src/python/gudhi/simplex_tree.pyx
+++ b/src/python/gudhi/simplex_tree.pyx
@@ -1,7 +1,3 @@
-from libc.stdint cimport intptr_t
-from numpy import array as np_array
-cimport simplex_tree
-
 # 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
@@ -11,6 +7,10 @@ cimport simplex_tree
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from libc.stdint cimport intptr_t
+from numpy import array as np_array
+cimport simplex_tree
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
@@ -508,7 +508,7 @@ cdef class SimplexTree:
         """
         if self.pcohptr != NULL:
             if persistence_file != '':
-                self.pcohptr.write_output_diagram(str.encode(persistence_file))
+                self.pcohptr.write_output_diagram(persistence_file.encode('utf-8'))
             else:
                 print("persistence_file must be specified")
         else:
diff --git a/src/python/gudhi/strong_witness_complex.pyx b/src/python/gudhi/strong_witness_complex.pyx
index 66d49b49..9f89d3ae 100644
--- a/src/python/gudhi/strong_witness_complex.pyx
+++ b/src/python/gudhi/strong_witness_complex.pyx
@@ -1,11 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.utility cimport pair
-from libc.stdint cimport intptr_t
-
-from gudhi.simplex_tree cimport *
-from gudhi.simplex_tree import SimplexTree
-
 # 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
@@ -15,6 +7,14 @@ from gudhi.simplex_tree import SimplexTree
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.utility cimport pair
+from libc.stdint cimport intptr_t
+
+from gudhi.simplex_tree cimport *
+from gudhi.simplex_tree import SimplexTree
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
@@ -22,9 +22,9 @@ __license__ = "MIT"
 cdef extern from "Strong_witness_complex_interface.h" namespace "Gudhi":
     cdef cppclass Strong_witness_complex_interface "Gudhi::witness_complex::Strong_witness_complex_interface":
         Strong_witness_complex_interface(vector[vector[pair[size_t, double]]] nearest_landmark_table)
-        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square)
+        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square) except +
         void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square,
-            unsigned limit_dimension)
+            unsigned limit_dimension) except +
 
 # StrongWitnessComplex python interface
 cdef class StrongWitnessComplex:
diff --git a/src/python/gudhi/subsampling.pyx b/src/python/gudhi/subsampling.pyx
index e0cd1348..f77c6f75 100644
--- a/src/python/gudhi/subsampling.pyx
+++ b/src/python/gudhi/subsampling.pyx
@@ -1,9 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.string cimport string
-from libcpp cimport bool
-import os
-
 # 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
@@ -13,6 +7,12 @@ import os
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.string cimport string
+from libcpp cimport bool
+import os
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "GPL v3"
@@ -33,13 +33,15 @@ def choose_n_farthest_points(points=None, off_file='', nb_points=0, starting_poi
     The iteration starts with the landmark `starting point`.
 
     :param points: The input point set.
-    :type points: vector[vector[double]].
+    :type points: Iterable[Iterable[float]].
 
     Or
 
     :param off_file: An OFF file style name.
     :type off_file: string
 
+    And in both cases
+
     :param nb_points: Number of points of the subsample.
     :type nb_points: unsigned.
     :param starting_point: The iteration starts with the landmark `starting \
@@ -47,15 +49,15 @@ def choose_n_farthest_points(points=None, off_file='', nb_points=0, starting_poi
     index is chosen randomly.
     :type starting_point: unsigned.
     :returns:  The subsample point set.
-    :rtype: vector[vector[double]]
+    :rtype: List[List[float]].
     """
     if off_file:
         if os.path.isfile(off_file):
             if starting_point == '':
-                return subsampling_n_farthest_points_from_file(str.encode(off_file),
+                return subsampling_n_farthest_points_from_file(off_file.encode('utf-8'),
                                                                nb_points)
             else:
-                return subsampling_n_farthest_points_from_file(str.encode(off_file),
+                return subsampling_n_farthest_points_from_file(off_file.encode('utf-8'),
                                                                nb_points,
                                                                starting_point)
         else:
@@ -74,21 +76,23 @@ def pick_n_random_points(points=None, off_file='', nb_points=0):
     """Subsample a point set by picking random vertices.
 
     :param points: The input point set.
-    :type points: vector[vector[double]].
+    :type points: Iterable[Iterable[float]].
 
     Or
 
     :param off_file: An OFF file style name.
     :type off_file: string
 
+    And in both cases
+
     :param nb_points: Number of points of the subsample.
     :type nb_points: unsigned.
     :returns:  The subsample point set.
-    :rtype: vector[vector[double]]
+    :rtype: List[List[float]]
     """
     if off_file:
         if os.path.isfile(off_file):
-            return subsampling_n_random_points_from_file(str.encode(off_file),
+            return subsampling_n_random_points_from_file(off_file.encode('utf-8'),
                 nb_points)
         else:
             print("file " + off_file + " not found.")
@@ -103,22 +107,24 @@ def sparsify_point_set(points=None, off_file='', min_squared_dist=0.0):
     between any two points is greater than or equal to min_squared_dist.
 
     :param points: The input point set.
-    :type points: vector[vector[double]].
+    :type points: Iterable[Iterable[float]].
 
     Or
 
     :param off_file: An OFF file style name.
     :type off_file: string
 
+    And in both cases
+
     :param min_squared_dist: Minimum squared distance separating the output \
     points.
     :type min_squared_dist: float.
     :returns:  The subsample point set.
-    :rtype: vector[vector[double]]
+    :rtype: List[List[float]]
     """
     if off_file:
         if os.path.isfile(off_file):
-            return subsampling_sparsify_points_from_file(str.encode(off_file),
+            return subsampling_sparsify_points_from_file(off_file.encode('utf-8'),
                                                          min_squared_dist)
         else:
             print("file " + off_file + " not found.")
diff --git a/src/python/gudhi/tangential_complex.pyx b/src/python/gudhi/tangential_complex.pyx
index f4c8b079..6391488c 100644
--- a/src/python/gudhi/tangential_complex.pyx
+++ b/src/python/gudhi/tangential_complex.pyx
@@ -1,3 +1,12 @@
+# 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
+
 from cython cimport numeric
 from libcpp.vector cimport vector
 from libcpp.utility cimport pair
@@ -9,15 +18,6 @@ import os
 from gudhi.simplex_tree cimport *
 from gudhi.simplex_tree import SimplexTree
 
-# 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) 2016 Inria"
 __license__ = "GPL v3"
@@ -66,7 +66,7 @@ cdef class TangentialComplex:
     def __cinit__(self, intrisic_dim, points=None, off_file=''):
         if off_file:
             if os.path.isfile(off_file):
-                self.thisptr = new Tangential_complex_interface(intrisic_dim, str.encode(off_file), True)
+                self.thisptr = new Tangential_complex_interface(intrisic_dim, off_file.encode('utf-8'), True)
             else:
                 print("file " + off_file + " not found.")
         else:
diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py
index d8a3104c..13102094 100644
--- a/src/python/gudhi/wasserstein.py
+++ b/src/python/gudhi/wasserstein.py
@@ -1,10 +1,3 @@
-import numpy as np
-import scipy.spatial.distance as sc
-try:
-    import ot
-except ImportError:
-    print("POT (Python Optimal Transport) package is not installed. Try to run $ conda install -c conda-forge pot ; or $ pip install POT")
-
 # 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):       Theo Lacombe
@@ -14,6 +7,13 @@ except ImportError:
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+import numpy as np
+import scipy.spatial.distance as sc
+try:
+    import ot
+except ImportError:
+    print("POT (Python Optimal Transport) package is not installed. Try to run $ conda install -c conda-forge pot ; or $ pip install POT")
+
 def _proj_on_diag(X):
     '''
     :param X: (n x 2) array encoding the points of a persistent diagram.
@@ -23,26 +23,26 @@ def _proj_on_diag(X):
     return np.array([Z , Z]).T
 
 
-def _build_dist_matrix(X, Y, p=2., q=2.):
+def _build_dist_matrix(X, Y, order=2., internal_p=2.):
     '''
     :param X: (n x 2) numpy.array encoding the (points of the) first diagram.
     :param Y: (m x 2) numpy.array encoding the second diagram.
-    :param q: Ground metric (i.e. norm l_q).
-    :param p: exponent for the Wasserstein metric.
+    :param order: exponent for the Wasserstein metric.
+    :param internal_p: Ground metric (i.e. norm L^p).
     :returns: (n+1) x (m+1) np.array encoding the cost matrix C. 
                 For 1 <= i <= n, 1 <= j <= m, C[i,j] encodes the distance between X[i] and Y[j], while C[i, m+1] (resp. C[n+1, j]) encodes the distance (to the p) between X[i] (resp Y[j]) and its orthogonal proj onto the diagonal.
                 note also that C[n+1, m+1] = 0  (it costs nothing to move from the diagonal to the diagonal).
     '''
     Xdiag = _proj_on_diag(X)
     Ydiag = _proj_on_diag(Y)
-    if np.isinf(q):
-        C = sc.cdist(X,Y, metric='chebyshev')**p
-        Cxd = np.linalg.norm(X - Xdiag, ord=q, axis=1)**p
-        Cdy = np.linalg.norm(Y - Ydiag, ord=q, axis=1)**p
+    if np.isinf(internal_p):
+        C = sc.cdist(X,Y, metric='chebyshev')**order
+        Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order
+        Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**order
     else:
-        C = sc.cdist(X,Y, metric='minkowski', p=q)**p
-        Cxd = np.linalg.norm(X - Xdiag, ord=q, axis=1)**p
-        Cdy = np.linalg.norm(Y - Ydiag, ord=q, axis=1)**p
+        C = sc.cdist(X,Y, metric='minkowski', p=internal_p)**order
+        Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order
+        Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**order
     Cf = np.hstack((C, Cxd[:,None]))
     Cdy = np.append(Cdy, 0)
 
@@ -51,24 +51,24 @@ def _build_dist_matrix(X, Y, p=2., q=2.):
     return Cf
 
 
-def _perstot(X, p, q):
+def _perstot(X, order, internal_p):
     '''
     :param X: (n x 2) numpy.array (points of a given diagram).
-    :param q: Ground metric on the (upper-half) plane (i.e. norm l_q in R^2); Default value is 2 (Euclidean norm).
-    :param p: exponent for Wasserstein; Default value is 2.
+    :param order: exponent for Wasserstein. Default value is 2.
+    :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); Default value is 2 (Euclidean norm).
     :returns: float, the total persistence of the diagram (that is, its distance to the empty diagram).    
     '''
     Xdiag = _proj_on_diag(X)
-    return (np.sum(np.linalg.norm(X - Xdiag, ord=q, axis=1)**p))**(1./p)
+    return (np.sum(np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order))**(1./order)
 
 
-def wasserstein_distance(X, Y, p=2., q=2.):
+def wasserstein_distance(X, Y, order=2., internal_p=2.):
     '''
     :param X: (n x 2) numpy.array encoding the (finite points of the) first diagram. Must not contain essential points (i.e. with infinite coordinate).
     :param Y: (m x 2) numpy.array encoding the second diagram.
-    :param q: Ground metric on the (upper-half) plane (i.e. norm l_q in R^2); Default value is 2 (euclidean norm).
-    :param p: exponent for Wasserstein; Default value is 2.
-    :returns: the p-Wasserstein distance (1 <= p < infinity) with respect to the q-norm as ground metric.
+    :param order: exponent for Wasserstein; Default value is 2.
+    :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); Default value is 2 (Euclidean norm).
+    :returns: the Wasserstein distance of order q (1 <= q < infinity) between persistence diagrams with respect to the internal_p-norm as ground metric.
     :rtype: float
     '''
     n = len(X)
@@ -79,20 +79,19 @@ def wasserstein_distance(X, Y, p=2., q=2.):
         if Y.size == 0:
             return 0.
         else:
-            return _perstot(Y, p, q)
+            return _perstot(Y, order, internal_p)
     elif Y.size == 0:
-        return _perstot(X, p, q)
+        return _perstot(X, order, internal_p)
 
-    M = _build_dist_matrix(X, Y, p=p, q=q)
+    M = _build_dist_matrix(X, Y, order=order, internal_p=internal_p)
     a = np.full(n+1, 1. / (n + m) )  # weight vector of the input diagram. Uniform here.
     a[-1] = a[-1] * m                # normalized so that we have a probability measure, required by POT
     b = np.full(m+1, 1. / (n + m) )  # weight vector of the input diagram. Uniform here.
     b[-1] = b[-1] * n                # so that we have a probability measure, required by POT
 
     # Comptuation of the otcost using the ot.emd2 library.
-    # Note: it is the squared Wasserstein distance.
+    # Note: it is the Wasserstein distance to the power q.
     # The default numItermax=100000 is not sufficient for some examples with 5000 points, what is a good value?
     ot_cost = (n+m) * ot.emd2(a, b, M, numItermax=2000000)
 
-    return ot_cost ** (1./p)
-
+    return ot_cost ** (1./order)
diff --git a/src/python/gudhi/witness_complex.pyx b/src/python/gudhi/witness_complex.pyx
index 153fc615..e589d006 100644
--- a/src/python/gudhi/witness_complex.pyx
+++ b/src/python/gudhi/witness_complex.pyx
@@ -1,11 +1,3 @@
-from cython cimport numeric
-from libcpp.vector cimport vector
-from libcpp.utility cimport pair
-from libc.stdint cimport intptr_t
-
-from gudhi.simplex_tree cimport *
-from gudhi.simplex_tree import SimplexTree
-
 # 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
@@ -15,6 +7,14 @@ from gudhi.simplex_tree import SimplexTree
 # Modification(s):
 #   - YYYY/MM Author: Description of the modification
 
+from cython cimport numeric
+from libcpp.vector cimport vector
+from libcpp.utility cimport pair
+from libc.stdint cimport intptr_t
+
+from gudhi.simplex_tree cimport *
+from gudhi.simplex_tree import SimplexTree
+
 __author__ = "Vincent Rouvreau"
 __copyright__ = "Copyright (C) 2016 Inria"
 __license__ = "MIT"
@@ -22,9 +22,9 @@ __license__ = "MIT"
 cdef extern from "Witness_complex_interface.h" namespace "Gudhi":
     cdef cppclass Witness_complex_interface "Gudhi::witness_complex::Witness_complex_interface":
         Witness_complex_interface(vector[vector[pair[size_t, double]]] nearest_landmark_table)
-        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square)
+        void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square) except +
         void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square,
-            unsigned limit_dimension)
+            unsigned limit_dimension) except +
 
 # WitnessComplex python interface
 cdef class WitnessComplex: