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diff --git a/doc/Witness_complex/COPYRIGHT b/doc/Witness_complex/COPYRIGHT
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-The files of this directory are part of the Gudhi Library. The Gudhi library
-(Geometric Understanding in Higher Dimensions) is a generic C++ library for
-computational topology.
-
-Author(s): Siargey Kachanovich
-
-Copyright (C) 2015 Inria
-
-This program is free software: you can redistribute it and/or modify it under
-the terms of the GNU General Public License as published by the Free Software
-Foundation, either version 3 of the License, or (at your option) any later
-version.
-
-This program is distributed in the hope that it will be useful, but WITHOUT
-ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
-FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
-
-You should have received a copy of the GNU General Public License along with
-this program. If not, see <http://www.gnu.org/licenses/>.
diff --git a/doc/Witness_complex/Witness_complex_doc.h b/doc/Witness_complex/Witness_complex_doc.h
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index 62203054..00000000
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-#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 witnessdefinitions Definitions
-
- Witness complex 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$L\f$ set of **landmarks**.
-
- Even though often the set of landmarks \f$L\f$ is a subset of the set of witnesses \f$ W\f$, it is not a requirement for the current implementation.
-
- Landmarks are the vertices of the simplicial complex
- and witnesses help to decide on which simplices are inserted via a predicate "is witnessed".
-
- De Silva and Carlsson in their paper \cite de2004topological differentiate **weak witnessing** and **strong witnessing**:
-
- - *weak*: \f$ \sigma \subset L \f$ is witnessed by \f$ w \in W\f$ if \f$ \forall l \in \sigma,\ \forall l' \in \mathbf{L \setminus \sigma},\ d(w,l) \leq d(w,l') \f$
- - *strong*: \f$ \sigma \subset L \f$ is witnessed by \f$ w \in W\f$ if \f$ \forall l \in \sigma,\ \forall l' \in \mathbf{L},\ d(w,l) \leq d(w,l') \f$
-
- where \f$ d(.,.) \f$ is a distance function.
-
- Both definitions can be relaxed by a real value \f$\alpha\f$:
-
- - *weak*: \f$ \sigma \subset L \f$ is \f$\alpha\f$-witnessed by \f$ w \in W\f$ if \f$ \forall l \in \sigma,\ \forall l' \in \mathbf{L \setminus \sigma},\ d(w,l)^2 \leq d(w,l')^2 + \alpha^2 \f$
- - *strong*: \f$ \sigma \subset L \f$ is \f$\alpha\f$-witnessed by \f$ w \in W\f$ if \f$ \forall l \in \sigma,\ \forall l' \in \mathbf{L},\ d(w,l)^2 \leq d(w,l')^2 + \alpha^2 \f$
-
- which leads to definitions of **weak relaxed witness complex** (or just relaxed witness complex for short) and **strong relaxed witness complex** respectively.
-
- \image html "swit.svg" "Strongly witnessed simplex"
-
- In particular case of 0-relaxation, weak complex corresponds to **witness complex** introduced in \cite de2004topological, whereas 0-relaxed strong witness complex consists of just vertices and is not very interesting.
- Hence for small relaxation weak version is preferable.
- However, to capture the homotopy type (for example using Gudhi::persistent_cohomology::Persistent_cohomology) it is often necessary to work with higher filtration values. In this case strong relaxed witness complex is faster to compute and offers similar results.
-
- \section witnessimplementation Implementation
-
- The two complexes described above are implemented in the corresponding classes
- - Gudhi::witness_complex::Witness_complex
- - Gudhi::witness_complex::Euclidean_witness_complex
- - Gudhi::witness_complex::Strong_witness_complex
- - Gudhi::witness_complex::Euclidean_strong_witness_complex
-
- The construction of the Euclidean versions of complexes follow the same scheme:
- 1. Construct a search tree on landmarks (for that Gudhi::spatial_searching::Kd_tree_search is used internally).
- 2. Construct lists of nearest landmarks for each witness (special structure Gudhi::witness_complex::Active_witness is used internally).
- 3. Construct the witness complex for nearest landmark lists.
-
- In the non-Euclidean classes, the lists of nearest landmarks are supposed to be given as input.
-
- The constructors take on the steps 1 and 2, while the function 'create_complex' executes the step 3.
-
- \section witnessexample1 Example 1: Constructing weak relaxed witness complex from an off file
-
- Let's start with a simple example, which reads an off point file and computes a weak witness complex.
-
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
-
-#include <gudhi/Simplex_tree.h>
-#include <gudhi/Euclidean_witness_complex.h>
-#include <gudhi/pick_n_random_points.h>
-#include <gudhi/Points_off_io.h>
-
-#include <CGAL/Epick_d.h>
-
-#include <string>
-#include <vector>
-
-typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
-typedef typename K::Point_d Point_d;
-typedef typename Gudhi::witness_complex::Euclidean_witness_complex<K> Witness_complex;
-typedef std::vector< Vertex_handle > typeVectorVertex;
-typedef std::vector< Point_d > Point_vector;
-
-int main(int argc, char * const argv[]) {
- std::string file_name = argv[1];
- int nbL = atoi(argv[2]), lim_dim = atoi(argv[4]);
- double alpha2 = atof(argv[3]);
- Gudhi::Simplex_tree<> simplex_tree;
-
- // Read the point file
- Point_vector point_vector, landmarks;
- Gudhi::Points_off_reader<Point_d> off_reader(file_name);
- point_vector = Point_vector(off_reader.get_point_cloud());
-
- // Choose landmarks (one can choose either of the two methods below)
- // Gudhi::subsampling::pick_n_random_points(point_vector, nbL, std::back_inserter(landmarks));
- Gudhi::subsampling::choose_n_farthest_points(K(), point_vector, nbL, Gudhi::subsampling::random_starting_point, std::back_inserter(landmarks));
-
- // Compute witness complex
- Witness_complex witness_complex(landmarks,
- point_vector);
-
- witness_complex.create_complex(simplex_tree, alpha2, lim_dim);
-}
-
-
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
- \section witnessexample2 Example2: Computing persistence using strong relaxed witness complex
-
- Here is an example of constructing a strong witness complex filtration and computing persistence on it:
-
- \include Witness_complex/strong_witness_persistence.cpp
-
- \section witnessexample3 Example3: Computing relaxed witness complex persistence from a distance matrix
-
- In this example we compute the relaxed witness complex persistence from a given matrix of closest landmarks to each witness.
- Each landmark is given as the couple (index, distance).
-
- \include Witness_complex/example_nearest_landmark_table.cpp
-
- */
-
-#endif // WITNESS_COMPLEX_DOC_H_
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