Merge branch 'master' into print_warnings_to_stderr

19 files changed, 165 insertions, 169 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 24e36bea..db11416c 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
@@ -9,15 +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"
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 b7047d4f..92ff6411 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
-
-import numpy as np
-
 # 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 @@ import numpy as np
 # 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"
diff --git a/src/python/gudhi/euclidean_strong_witness_complex.pyx b/src/python/gudhi/euclidean_strong_witness_complex.pyx
index e3f451f0..9889f92c 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"
diff --git a/src/python/gudhi/euclidean_witness_complex.pyx b/src/python/gudhi/euclidean_witness_complex.pyx
index 84a8ea1a..e3ce0e82 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"
diff --git a/src/python/gudhi/nerve_gic.pyx b/src/python/gudhi/nerve_gic.pyx
index acb78564..68c06432 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"
diff --git a/src/python/gudhi/off_reader.pyx b/src/python/gudhi/off_reader.pyx
index 225e981c..58f05db8 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"
@@ -19,7 +19,7 @@ __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.
diff --git a/src/python/gudhi/periodic_cubical_complex.pyx b/src/python/gudhi/periodic_cubical_complex.pyx
index eb96ab5f..b5dece10 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
-
-import numpy as np
-
 # 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 @@ import numpy as np
 # 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"
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..345c92f8 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"
diff --git a/src/python/gudhi/rips_complex.pyx b/src/python/gudhi/rips_complex.pyx
index cbbbab0d..722cdcdc 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"
diff --git a/src/python/gudhi/simplex_tree.pxd b/src/python/gudhi/simplex_tree.pxd
index 5f86cfe2..1066d44b 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"
diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx
index 4a3cd9bc..85d25492 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"
diff --git a/src/python/gudhi/strong_witness_complex.pyx b/src/python/gudhi/strong_witness_complex.pyx
index 66d49b49..2c33c3f2 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"
diff --git a/src/python/gudhi/subsampling.pyx b/src/python/gudhi/subsampling.pyx
index e0cd1348..b1812087 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"
diff --git a/src/python/gudhi/tangential_complex.pyx b/src/python/gudhi/tangential_complex.pyx
index f4c8b079..0083033c 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"
diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py
index d8a3104c..db5ddff2 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 internal_p: Ground metric (i.e. norm l_p).
+    :param order: exponent for the Wasserstein metric.
     :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 internal_p: Ground metric on the (upper-half) plane (i.e. norm l_p in R^2); Default value is 2 (Euclidean norm).
+    :param order: exponent for Wasserstein. Default value is 2.
     :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 internal_p: Ground metric on the (upper-half) plane (i.e. norm l_p in R^2); Default value is 2 (euclidean norm).
+    :param order: exponent for Wasserstein; Default value is 2.
+    :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..b032a5a1 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"