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#ifndef WITNESS_COMPLEX_DOC_
#define WITNESS_COMPLEX_DOC_
/**
\defgroup witness_complex Witness complex
\author Siargey Kachanovich
\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.
\section Implementation
Two classes are implemented in this module: Gudhi::Witness_complex and Gudhi::Relaxed_witness_complex.
While Gudhi::Witness_complex represents the classical witness complex, Gudhi::Relaxed_witness_complex takes an additional positive real parameter \f$ \alpha \f$ and constructs simplices \f$ \sigma \f$, for which
there exists \f$ w \in W \f$, such that \f$ d(p,w) < d(q,w) + \alpha \f$ for all \f$ p \in \sigma, q \in L\setminus \sigma \f$.
In both cases, the constructors take a {witness}x{closest_landmarks} table,
which can be constructed by two additional classes Landmark_choice_by_furthest_point and Landmark_choice_by_random_point also included in the module.
\copyright GNU General Public License v3.
*/
#endif
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