Add bottleneck distance

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@2019 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 1320379f3d41ef4d11326c1aad1dd20469d3f4e0

4 files changed, 62 insertions, 0 deletions

diff --git a/src/cython/doc/bottleneck_distance_ref.rst b/src/cython/doc/bottleneck_distance_ref.rst
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@@ -0,0 +1,5 @@
+===========================
+Bottleneck reference manual
+===========================
+
+.. automethod:: gudhi.bottleneck_distance
diff --git a/src/cython/doc/bottleneck_distance_sum.rst b/src/cython/doc/bottleneck_distance_sum.rst
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+=====================================  =====================================  =====================================
+:Author: Francois Godi                 :Introduced in: GUDHI 1.4.0            :Copyright: GPL v3
+=====================================  =====================================  =====================================
+:Requires: CGAL ≥ 4.8.0
+=====================================  =====================================  =====================================
+
++-------------------------------------------+----------------------------------------------------------------------+
+| .. image::                                | Bottleneck distance measures the similarity between two persistence  |
+|      img/perturb_pd.png                   | diagrams. It's the shortest distance b for which there exists a      |
+|                                           | perfect matching between the points of the two diagrams (+ all the   |
+|                                           | diagonal points) such that any couple of matched points are at       |
+|                                           | distance at most b.                                                  |
++-------------------------------------------+----------------------------------------------------------------------+
+| :doc:`bottleneck_distance_user`           | :doc:`bottleneck_distance_ref`                                       |
++-------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/bottleneck_distance_user.rst b/src/cython/doc/bottleneck_distance_user.rst
new file mode 100644
index 00000000..08c6e451
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+++ b/src/cython/doc/bottleneck_distance_user.rst
@@ -0,0 +1,37 @@
+===============================
+Bottleneck distance user manual
+===============================
+Definition
+----------
+
+.. include:: bottleneck_distance_sum.rst
+
+Function
+--------
+.. automethod:: gudhi.bottleneck_distance
+
+
+Basic example
+-------------
+
+This example computes the bottleneck distance from 2 persistence diagrams:
+
+.. testcode::
+
+    import gudhi
+
+    diag1 = [[2.7, 3.7],[9.6, 14.],[34.2, 34.974], [3.,float('Inf')]]
+    diag2 = [[2.8, 4.45],[9.5, 14.1],[3.2,float('Inf')]]
+
+    message = "Bottleneck distance approximation=" + repr(gudhi.bottleneck_distance(diag1, diag2, 0.1))
+    print(message)
+
+    message = "Bottleneck distance exact value=" + repr(gudhi.bottleneck_distance(diag1, diag2))
+    print(message)
+
+The output is:
+
+.. testoutput::
+
+    Bottleneck distance approximation=0.8081763781405569
+    Bottleneck distance exact value=0.75
diff --git a/src/cython/doc/index.rst b/src/cython/doc/index.rst
index 91e31ff6..de90cf7c 100644
--- a/src/cython/doc/index.rst
+++ b/src/cython/doc/index.rst
@@ -62,6 +62,11 @@ Witness complex
 Toolbox
 *******
 
+Bottleneck distance
+===================
+
+.. include:: bottleneck_distance_sum.rst
+
 Persistence cohomology
 ======================