Changeset 1276:b143e42c44de in lemon-0.x for src/demo

Timestamp:

03/30/05 16:29:11 (19 years ago)

Author:

marci

Branch:

default

Phase:

public

Convert:

svn:c9d7d8f5-90d6-0310-b91f-818b3a526b0e/lemon/trunk@1708

Message:

latex documentation for TightEdgeFilterMap?, including amsmath and amssymb latex
packages for latex documentation

File:

• src/demo/tight_edge_filter_map.h (modified) (2 diffs)

src/demo/tight_edge_filter_map.h

@@ -26 +26 @@
 namespace lemon {
 
-  /// \brief A map for filtering the edge-set to those edges 
-  /// which are tight w.r.t. some node_potential map and 
-  /// edge_distance map.
-  ///
-  /// A node-map node_potential is said to be a potential w.r.t. 
-  /// an edge-map edge_distance 
-  /// if and only if for each edge e, node_potential[g.target(e)] 
-  /// <= edge_distance[e]+node_potential[g.source(e)] 
-  /// (or the reverse inequality holds for each edge).
-  /// An edge is said to be tight if this inequality holds with equality, 
-  /// and the map returns true exactly for those edges.
-  /// To avoid rounding errors, it is recommended to use this class with exact 
-  /// types, e.g. with int.
+  /*! 
+    \brief A map for filtering the edge-set to those edges 
+    which are tight w.r.t. a node-potential and 
+    edge-distance.
+    
+    Let \f$G=(V,A)\f$ be a directed graph (graph for short) and 
+    let \f$\mathbb{F}\f$ be a number type. 
+    Given a distance function 
+    \f$d:E\to\mathbb{F}\f$, 
+    \f$\pi:V\to\mathbb{F}\f$ is said to be a potetial 
+    w.r.t. \f$d\f$ 
+    if and only if 
+    \f$\pi(v)\le d(uv)+\pi(u)\f$ holds for each edge \f$uv\in E\f$ 
+    (or the reverse inequality holds for each edge). 
+    An edge is said to be tight if this inequality holds with equality, 
+    and the map returns \c true exactly for those edges. 
+    To avoid rounding errors, it is recommended to use this class with exact 
+    number types, e.g. with \c int.
+  */
   template<typename Graph, 
            typename NodePotentialMap, typename EdgeDistanceMap>
@@ -60 +66 @@
 
 #endif //LEMON_TIGHT_EDGE_FILTER_MAP_H
-
-