latex documentation for TightEdgeFilterMap, including amsmath and amssymb latex
authormarci
Wed, 30 Mar 2005 14:29:11 +0000
changeset 1276b143e42c44de
parent 1275 16980bf77bd3
child 1277 e4cc8e996912
latex documentation for TightEdgeFilterMap, including amsmath and amssymb latex
packages for latex documentation
doc/Doxyfile
src/demo/tight_edge_filter_map.h
     1.1 --- a/doc/Doxyfile	Wed Mar 30 13:01:58 2005 +0000
     1.2 +++ b/doc/Doxyfile	Wed Mar 30 14:29:11 2005 +0000
     1.3 @@ -462,6 +462,7 @@
     1.4  			 gwrappers.dox \
     1.5                           ../src/lemon \
     1.6                           ../src/lemon/concept \
     1.7 +                         ../src/demo \
     1.8                           ../src/test/test_tools.h
     1.9  
    1.10  # If the value of the INPUT tag contains directories, you can use the 
    1.11 @@ -766,7 +767,8 @@
    1.12  # The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX 
    1.13  # packages that should be included in the LaTeX output.
    1.14  
    1.15 -EXTRA_PACKAGES         = 
    1.16 +EXTRA_PACKAGES         = amsmath \ 
    1.17 +			 amssymb
    1.18  
    1.19  # The LATEX_HEADER tag can be used to specify a personal LaTeX header for 
    1.20  # the generated latex document. The header should contain everything until 
     2.1 --- a/src/demo/tight_edge_filter_map.h	Wed Mar 30 13:01:58 2005 +0000
     2.2 +++ b/src/demo/tight_edge_filter_map.h	Wed Mar 30 14:29:11 2005 +0000
     2.3 @@ -25,19 +25,25 @@
     2.4  
     2.5  namespace lemon {
     2.6  
     2.7 -  /// \brief A map for filtering the edge-set to those edges 
     2.8 -  /// which are tight w.r.t. some node_potential map and 
     2.9 -  /// edge_distance map.
    2.10 -  ///
    2.11 -  /// A node-map node_potential is said to be a potential w.r.t. 
    2.12 -  /// an edge-map edge_distance 
    2.13 -  /// if and only if for each edge e, node_potential[g.target(e)] 
    2.14 -  /// <= edge_distance[e]+node_potential[g.source(e)] 
    2.15 -  /// (or the reverse inequality holds for each edge).
    2.16 -  /// An edge is said to be tight if this inequality holds with equality, 
    2.17 -  /// and the map returns true exactly for those edges.
    2.18 -  /// To avoid rounding errors, it is recommended to use this class with exact 
    2.19 -  /// types, e.g. with int.
    2.20 +  /*! 
    2.21 +    \brief A map for filtering the edge-set to those edges 
    2.22 +    which are tight w.r.t. a node-potential and 
    2.23 +    edge-distance.
    2.24 +    
    2.25 +    Let \f$G=(V,A)\f$ be a directed graph (graph for short) and 
    2.26 +    let \f$\mathbb{F}\f$ be a number type. 
    2.27 +    Given a distance function 
    2.28 +    \f$d:E\to\mathbb{F}\f$, 
    2.29 +    \f$\pi:V\to\mathbb{F}\f$ is said to be a potetial 
    2.30 +    w.r.t. \f$d\f$ 
    2.31 +    if and only if 
    2.32 +    \f$\pi(v)\le d(uv)+\pi(u)\f$ holds for each edge \f$uv\in E\f$ 
    2.33 +    (or the reverse inequality holds for each edge). 
    2.34 +    An edge is said to be tight if this inequality holds with equality, 
    2.35 +    and the map returns \c true exactly for those edges. 
    2.36 +    To avoid rounding errors, it is recommended to use this class with exact 
    2.37 +    number types, e.g. with \c int.
    2.38 +  */
    2.39    template<typename Graph, 
    2.40  	   typename NodePotentialMap, typename EdgeDistanceMap>
    2.41    class TightEdgeFilterMap : public MapBase<typename Graph::Edge, bool> {
    2.42 @@ -59,5 +65,3 @@
    2.43  } //namespace lemon
    2.44  
    2.45  #endif //LEMON_TIGHT_EDGE_FILTER_MAP_H
    2.46 -
    2.47 -