From 55c7181126aa7defce38c9b82872d14223d4c1dd Mon Sep 17 00:00:00 2001 From: Gard Spreemann Date: Tue, 7 Feb 2017 17:33:01 +0100 Subject: Initial import of upstream's 1.3.1. --- doc/Witness_complex/Witness_complex_doc.h | 42 +++++++++++++++++++++++++++++++ 1 file changed, 42 insertions(+) create mode 100644 doc/Witness_complex/Witness_complex_doc.h (limited to 'doc/Witness_complex/Witness_complex_doc.h') diff --git a/doc/Witness_complex/Witness_complex_doc.h b/doc/Witness_complex/Witness_complex_doc.h new file mode 100644 index 00000000..60dfd27b --- /dev/null +++ b/doc/Witness_complex/Witness_complex_doc.h @@ -0,0 +1,42 @@ +#ifndef WITNESS_COMPLEX_DOC_H_ +#define WITNESS_COMPLEX_DOC_H_ + +/** + \defgroup witness_complex Witness complex + + \author Siargey Kachanovich + + \image html "Witness_complex_representation.png" "Witness complex representation" + + \section Definitions + + Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$: + + \li \f$W\f$ set of **witnesses** and + \li \f$L \subseteq W\f$ set of **landmarks**. + + The simplices are based on landmarks + and a simplex belongs to the witness complex if and only if it is witnessed, that is: + + \f$ \sigma \subset L \f$ is witnessed if there exists a point \f$w \in W\f$ such that + w is closer to the vertices of \f$ \sigma \f$ than other points in \f$ L \f$ and all of its faces are witnessed as well. + + The data structure is described in \cite boissonnatmariasimplextreealgorithmica . + + \section Implementation + + The principal class of this module is Gudhi::Witness_complex. + + In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a witness and consists of landmarks sorted by distance to this witness. + This table can be constructed by two additional classes Landmark_choice_by_furthest_point and Landmark_choice_by_random_point also included in the module. + + *\image html "bench_Cy8.png" "Running time as function on number of landmarks" width=10cm + *\image html "bench_sphere.png" "Running time as function on number of witnesses for |L|=300" width=10cm + + + \copyright GNU General Public License v3. + + + */ + +#endif // WITNESS_COMPLEX_DOC_H_ -- cgit v1.2.3