From 50f9bb7d06bbf98c128513399a8f951870b074be Mon Sep 17 00:00:00 2001 From: ROUVREAU Vincent Date: Tue, 2 Jun 2020 22:45:38 +0200 Subject: doc review: Move a sentence as a module summary --- src/Collapse/doc/intro_edge_collapse.h | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/src/Collapse/doc/intro_edge_collapse.h b/src/Collapse/doc/intro_edge_collapse.h index 82fadfb0..15f2208c 100644 --- a/src/Collapse/doc/intro_edge_collapse.h +++ b/src/Collapse/doc/intro_edge_collapse.h @@ -21,6 +21,10 @@ namespace collapse { * * @{ * + * This module implements edge collapse of a filtered flag complex, in particular it reduces a filtration of + * Vietoris-Rips complex from its graph to another smaller flag filtration with same persistence. + * Where a filtration is a sequence of simplicial (here Rips) complexes connected with inclusions. + * * \section edge_collapse_definition Edge collapse definition * * An edge \f$e\f$ in a simplicial complex \f$K\f$ is called a dominated edge if the link of \f$e\f$ in @@ -48,15 +52,11 @@ namespace collapse { * -- For a flag complex: An edge \f$e \in K\f$ is dominated by another vertex \f$v^{\prime} \in K\f$, if and only * if all the vertices in \f$K\f$ that has an edge with both vertices of \f$e\f$ also has an edge with * \f$v^{\prime}\f$. - - * This module implements edge collapse of a filtered flag complex, in particular it reduces a filtration of - * Vietoris-Rips complex from its graph - * to another smaller flag filtration with same persistence. Where a filtration is a sequence of simplicial - * (here Rips) complexes connected with inclusions. The algorithm to compute the smaller induced filtration is - * described in Section 5 \cite edgecollapsesocg2020. + * + * The algorithm to compute the smaller induced filtration is described in Section 5 \cite edgecollapsesocg2020. * Edge collapse can be successfully employed to reduce any given filtration of flag complexes to a smaller induced - * filtration which preserves the persistent homology of the original filtration and is a flag complex as well. - + * filtration which preserves the persistent homology of the original filtration and is a flag complex as well. + * * The general idea is that we consider edges in the filtered graph and sort them according to their filtration value * giving them a total order. * Each edge gets a unique index denoted as \f$i\f$ in this order. To reduce the filtration, we move forward with -- cgit v1.2.3