Tweaks to the doc of Bottleneck.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/bottleneck-doc-glisse@1983 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 5300e7c4cfd3ffe22fa7ec906a4193d99d95453b

2 files changed, 17 insertions, 6 deletions

diff --git a/src/Bottleneck_distance/include/gudhi/Bottleneck.h b/src/Bottleneck_distance/include/gudhi/Bottleneck.h
index b5641e29..b90a0ee0 100644
--- a/src/Bottleneck_distance/include/gudhi/Bottleneck.h
+++ b/src/Bottleneck_distance/include/gudhi/Bottleneck.h
@@ -80,11 +80,22 @@ double bottleneck_distance_exact(Persistence_graph& g) {
   return sd.at(lower_bound_i);
 }
 
-/** \brief Function to use in order to compute the Bottleneck distance between two persistence diagrams (see concepts).
- * If the last parameter e is not 0, you get an additive e-approximation, which is a lot faster to compute whatever is
- * e.
- * Thus, by default, e is a very small positive double, actually the smallest double possible such that the
- * floating-point inaccuracies don't lead to a failure of the algorithm.
+/** \brief Function to compute the Bottleneck distance between two persistence diagrams.
+ *
+ * \tparam Persistence_diagram1,Persistence_diagram2
+ * models of the concept `PersistenceDiagram`.
+ * \param[in] e
+ * \parblock
+ * If `e` is 0, this uses an expensive algorithm to compute the exact distance.
+ *
+ * If `e` is not 0, it asks for an additive `e`-approximation, and currently
+ * also allows a small multiplicative error (the last 2 or 3 bits of the
+ * mantissa may be wrong). This version of the algorithm takes advantage of the
+ * limited precision of `double` and is usually a lot faster to compute,
+ * whatever the value of `e`.
+ *
+ * Thus, by default, `e` is the smallest positive double.
+ * \endparblock
  *
  * \ingroup bottleneck_distance
  */
diff --git a/src/Bottleneck_distance/include/gudhi/Persistence_graph.h b/src/Bottleneck_distance/include/gudhi/Persistence_graph.h
index 39efc082..c7695112 100644
--- a/src/Bottleneck_distance/include/gudhi/Persistence_graph.h
+++ b/src/Bottleneck_distance/include/gudhi/Persistence_graph.h
@@ -40,7 +40,7 @@ namespace persistence_diagram {
  */
 class Persistence_graph {
  public:
-  /** \internal \brief Constructor taking 2 Persistence_Diagrams (concept) as parameters. */
+  /** \internal \brief Constructor taking 2 PersistenceDiagrams (concept) as parameters. */
   template<typename Persistence_diagram1, typename Persistence_diagram2>
   Persistence_graph(const Persistence_diagram1& diag1, const Persistence_diagram2& diag2, double e);
   /** \internal \brief Is the given point from U the projection of a point in V ? */