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authorGard Spreemann <gspr@nonempty.org>2019-09-25 14:29:41 +0200
committerGard Spreemann <gspr@nonempty.org>2019-09-25 14:29:41 +0200
commit599d68cd916f533bdb66dd9e684dd5703233b6bb (patch)
tree4b825dc642cb6eb9a060e54bf8d69288fbee4904 /doc
parenta2e642954ae39025e041471d486ecbac25dff440 (diff)
Delete all files in order to incorporate upstream's move to git.
Diffstat (limited to 'doc')
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diff --git a/doc/Alpha_complex/COPYRIGHT b/doc/Alpha_complex/COPYRIGHT
deleted file mode 100644
index 5f1d97cc..00000000
--- a/doc/Alpha_complex/COPYRIGHT
+++ /dev/null
@@ -1,19 +0,0 @@
-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): Vincent Rouvreau
-
-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/Alpha_complex/Intro_alpha_complex.h b/doc/Alpha_complex/Intro_alpha_complex.h
deleted file mode 100644
index 7a375c9f..00000000
--- a/doc/Alpha_complex/Intro_alpha_complex.h
+++ /dev/null
@@ -1,177 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Vincent Rouvreau
- *
- * 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/>.
- */
-
-#ifndef DOC_ALPHA_COMPLEX_INTRO_ALPHA_COMPLEX_H_
-#define DOC_ALPHA_COMPLEX_INTRO_ALPHA_COMPLEX_H_
-
-// needs namespace for Doxygen to link on classes
-namespace Gudhi {
-// needs namespace for Doxygen to link on classes
-namespace alpha_complex {
-
-/** \defgroup alpha_complex Alpha complex
- *
- * \author Vincent Rouvreau
- *
- * @{
- *
- * \section definition Definition
- *
- * Alpha_complex is a <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
- * constructed from the finite cells of a Delaunay Triangulation.
- *
- * The filtration value of each simplex is computed as the square of the circumradius of the simplex if the
- * circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration
- * values of the codimension 1 cofaces that make it not Gabriel otherwise.
- *
- * All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into
- * the complex.
- *
- * \image html "alpha_complex_representation.png" "Alpha-complex representation"
- *
- * Alpha_complex is constructing a <a target="_blank"
- * href="http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations">Delaunay Triangulation</a>
- * \cite cgal:hdj-t-15b from <a target="_blank" href="http://www.cgal.org/">CGAL</a> (the Computational Geometry
- * Algorithms Library \cite cgal:eb-15b) and is able to create a `SimplicialComplexForAlpha`.
- *
- * The complex is a template class requiring an Epick_d <a target="_blank"
- * href="http://doc.cgal.org/latest/Kernel_d/index.html#Chapter_dD_Geometry_Kernel">dD Geometry Kernel</a>
- * \cite cgal:s-gkd-15b from CGAL as template parameter.
- *
- * \remark
- * - When the simplicial complex is constructed with an infinite value of alpha, the complex is a Delaunay
- * complex.
- * - For people only interested in the topology of the \ref alpha_complex (for instance persistence),
- * \ref alpha_complex is equivalent to the \ref cech_complex and much smaller if you do not bound the radii.
- * \ref cech_complex can still make sense in higher dimension precisely because you can bound the radii.
- *
- * \section pointsexample Example from points
- *
- * This example builds the Delaunay triangulation from the given points in a 2D static kernel, and creates a
- * `Simplex_tree` with it.
- *
- * Then, it is asked to display information about the simplicial complex.
- *
- * \include Alpha_complex/Alpha_complex_from_points.cpp
- *
- * When launching:
- *
- * \code $> ./Alpha_complex_example_from_points
- * \endcode
- *
- * the program output is:
- *
- * \include Alpha_complex/alphaoffreader_for_doc_60.txt
- *
- * \section createcomplexalgorithm Create complex algorithm
- *
- * \subsection datastructure Data structure
- *
- * In order to create the simplicial complex, first, it is built from the cells of the Delaunay Triangulation.
- * The filtration values are set to NaN, which stands for unknown value.
- *
- * In example, :
- * \image html "alpha_complex_doc.png" "Simplicial complex structure construction example"
- *
- * \subsection filtrationcomputation Filtration value computation algorithm
- * <br>
- * \f$
- * \textbf{for } \text{i : dimension } \rightarrow 0 \textbf{ do}\\
- * \quad \textbf{for all } \sigma \text{ of dimension i}\\
- * \quad\quad \textbf{if } \text{filtration(} \sigma ) \text{ is NaN} \textbf{ then}\\
- * \quad\quad\quad \text{filtration(} \sigma ) = \alpha^2( \sigma )\\
- * \quad\quad \textbf{end if}\\
- * \quad\quad \textbf{for all } \tau \text{ face of } \sigma \textbf{ do}\quad\quad
- * \textit{// propagate alpha filtration value}\\
- * \quad\quad\quad \textbf{if } \text{filtration(} \tau ) \text{ is not NaN} \textbf{ then}\\
- * \quad\quad\quad\quad \text{filtration(} \tau \text{) = min( filtration(} \tau \text{), filtration(} \sigma
- * \text{) )}\\
- * \quad\quad\quad \textbf{else}\\
- * \quad\quad\quad\quad \textbf{if } \textbf{if } \tau \text{ is not Gabriel for } \sigma \textbf{ then}\\
- * \quad\quad\quad\quad\quad \text{filtration(} \tau \text{) = filtration(} \sigma \text{)}\\
- * \quad\quad\quad\quad \textbf{end if}\\
- * \quad\quad\quad \textbf{end if}\\
- * \quad\quad \textbf{end for}\\
- * \quad \textbf{end for}\\
- * \textbf{end for}\\
- * \text{make_filtration_non_decreasing()}\\
- * \text{prune_above_filtration()}\\
- * \f$
- *
- * \subsubsection dimension2 Dimension 2
- *
- * From the example above, it means the algorithm looks into each triangle ([0,1,2], [0,2,4], [1,2,3], ...),
- * computes the filtration value of the triangle, and then propagates the filtration value as described
- * here :
- * \image html "alpha_complex_doc_420.png" "Filtration value propagation example"
- *
- * \subsubsection dimension1 Dimension 1
- *
- * Then, the algorithm looks into each edge ([0,1], [0,2], [1,2], ...),
- * computes the filtration value of the edge (in this case, propagation will have no effect).
- *
- * \subsubsection dimension0 Dimension 0
- *
- * Finally, the algorithm looks into each vertex ([0], [1], [2], [3], [4], [5] and [6]) and
- * sets the filtration value (0 in case of a vertex - propagation will have no effect).
- *
- * \subsubsection nondecreasing Non decreasing filtration values
- *
- * As the squared radii computed by CGAL are an approximation, it might happen that these alpha squared values do not
- * quite define a proper filtration (i.e. non-decreasing with respect to inclusion).
- * We fix that up by calling `SimplicialComplexForAlpha::make_filtration_non_decreasing()`.
- *
- * \subsubsection pruneabove Prune above given filtration value
- *
- * The simplex tree is pruned from the given maximum alpha squared value (cf.
- * `SimplicialComplexForAlpha::prune_above_filtration()`).
- * In the following example, the value is given by the user as argument of the program.
- *
- *
- * \section offexample Example from OFF file
- *
- * This example builds the Delaunay triangulation in a dynamic kernel, and initializes the alpha complex with it.
- *
- *
- * Then, it is asked to display information about the alpha complex.
- *
- * \include Alpha_complex/Alpha_complex_from_off.cpp
- *
- * When launching:
- *
- * \code $> ./Alpha_complex_example_from_off ../../data/points/alphacomplexdoc.off 32.0
- * \endcode
- *
- * the program output is:
- *
- * \include Alpha_complex/alphaoffreader_for_doc_32.txt
- *
- */
-/** @} */ // end defgroup alpha_complex
-
-} // namespace alpha_complex
-
-namespace alphacomplex = alpha_complex;
-
-} // namespace Gudhi
-
-#endif // DOC_ALPHA_COMPLEX_INTRO_ALPHA_COMPLEX_H_
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diff --git a/doc/Alpha_complex/alpha_complex_representation.png b/doc/Alpha_complex/alpha_complex_representation.png
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diff --git a/doc/Bitmap_cubical_complex/COPYRIGHT b/doc/Bitmap_cubical_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): Pawel Dlotko
-
-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.
-
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diff --git a/doc/Bitmap_cubical_complex/Cubical_complex_representation.png b/doc/Bitmap_cubical_complex/Cubical_complex_representation.png
deleted file mode 100644
index afb2a75e..00000000
--- a/doc/Bitmap_cubical_complex/Cubical_complex_representation.png
+++ /dev/null
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diff --git a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h
deleted file mode 100644
index d1836ef0..00000000
--- a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h
+++ /dev/null
@@ -1,117 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Pawel Dlotko
- *
- * 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/>.
- */
-
-
-#ifndef DOC_GUDHI_CUBICAL_COMPLEX_COMPLEX_H_
-#define DOC_GUDHI_CUBICAL_COMPLEX_COMPLEX_H_
-
-namespace Gudhi {
-
-namespace cubical_complex {
-
-/** \defgroup cubical_complex Cubical complex
- *
- * \author Pawel Dlotko
- *
- * @{
- *
-
- * Bitmap_cubical_complex is an example of a structured complex useful in computational mathematics (specially rigorous
- * numerics) and image analysis. The presented implementation of cubical complexes is based on the following
- * definition.
- *
- * An <em>elementary interval</em> is an interval of a form \f$ [n,n+1] \f$, or \f$[n,n]\f$, for \f$ n \in \mathcal{Z}
- * \f$. The first one is called <em>non-degenerate</em>, while the second one is \a degenerate interval. A
- * <em>boundary of a elementary interval</em> is a chain \f$\partial [n,n+1] = [n+1,n+1]-[n,n] \f$ in case of
- * non-degenerated elementary interval and \f$\partial [n,n] = 0 \f$ in case of degenerate elementary interval. An
- * <em>elementary cube</em> \f$ C \f$ is a product of elementary intervals, \f$C=I_1 \times \ldots \times I_n\f$.
- * <em>Embedding dimension</em> of a cube is n, the number of elementary intervals (degenerate or not) in the product.
- * A <em>dimension of a cube</em> \f$C=I_1 \times ... \times I_n\f$ is the number of non degenerate elementary
- * intervals in the product. A <em>boundary of a cube</em> \f$C=I_1 \times \ldots \times I_n\f$ is a chain obtained
- * in the following way:
- * \f[\partial C = (\partial I_1 \times \ldots \times I_n) + (I_1 \times \partial I_2 \times \ldots \times I_n) +
- * \ldots + (I_1 \times I_2 \times \ldots \times \partial I_n).\f]
- * A <em>cubical complex</em> \f$\mathcal{K}\f$ is a collection of cubes closed under operation of taking boundary
- * (i.e. boundary of every cube from the collection is in the collection). A cube \f$C\f$ in cubical complex
- * \f$\mathcal{K}\f$ is <em>maximal</em> if it is not in a boundary of any other cube in \f$\mathcal{K}\f$. A \a
- * support of a cube \f$C\f$ is the set in \f$\mathbb{R}^n\f$ occupied by \f$C\f$ (\f$n\f$ is the embedding dimension
- * of \f$C\f$).
- *
- * Cubes may be equipped with a filtration values in which case we have filtered cubical complex. All the cubical
- * complexes considered in this implementation are filtered cubical complexes (although, the range of a filtration may
- * be a set of two elements).
- *
- * For further details and theory of cubical complexes, please consult \cite kaczynski2004computational as well as the
- * following paper \cite peikert2012topological .
- *
- * \section cubicalcomplexdatastructure Data structure
- *
- * The implementation of Cubical complex provides a representation of complexes that occupy a rectangular region in
- * \f$\mathbb{R}^n\f$. This extra assumption allows for a memory efficient way of storing cubical complexes in a form
- * of so called bitmaps. Let \f$R = [b_1,e_1] \times \ldots \times [b_n,e_n]\f$, for \f$b_1,...b_n,e_1,...,e_n \in
- * \mathbb{Z}\f$, \f$b_i \leq d_i\f$ be the considered rectangular region and let \f$\mathcal{K}\f$ be a filtered
- * cubical complex having the rectangle \f$R\f$ as its support. Note that the structure of the coordinate system gives
- * a way a lexicographical ordering of cells of \f$\mathcal{K}\f$. This ordering is a base of the presented
- * bitmap-based implementation. In this implementation, the whole cubical complex is stored as a vector of the values
- * of filtration. This, together with dimension of \f$\mathcal{K}\f$ and the sizes of \f$\mathcal{K}\f$ in all
- * directions, allows to determine, dimension, neighborhood, boundary and coboundary of every cube \f$C \in
- * \mathcal{K}\f$.
- *
- * \image html "Cubical_complex_representation.png" Cubical complex.
- *
- * Note that the cubical complex in the figure above is, in a natural way, a product of one dimensional cubical
- * complexes in \f$\mathbb{R}\f$. The number of all cubes in each direction is equal \f$2n+1\f$, where \f$n\f$ is the
- * number of maximal cubes in the considered direction. Let us consider a cube at the position \f$k\f$ in the bitmap.
- * Knowing the sizes of the bitmap, by a series of modulo operation, we can determine which elementary intervals are
- * present in the product that gives the cube \f$C\f$. In a similar way, we can compute boundary and the coboundary of
- * each cube. Further details can be found in the literature.
- *
- * \section inputformat Input Format
- *
- * In the current implantation, filtration is given at the maximal cubes, and it is then extended by the lower star
- * filtration to all cubes. There are a number of constructors that can be used to construct cubical complex by users
- * who want to use the code directly. They can be found in the \a Bitmap_cubical_complex class.
- * Currently one input from a text file is used. It uses a format used already in Perseus software
- * (http://www.sas.upenn.edu/~vnanda/perseus/) by Vidit Nanda. The file format is described here: \ref FileFormatsPerseus.
- *
- * \section PeriodicBoundaryConditions Periodic boundary conditions
- * Often one would like to impose periodic boundary conditions to the cubical complex. Let \f$ I_1\times ... \times
- * I_n \f$ be a box that is decomposed with a cubical complex \f$ \mathcal{K} \f$. Imposing periodic boundary
- * conditions in the direction i, means that the left and the right side of a complex \f$ \mathcal{K} \f$ are
- * considered the same. In particular, if for a bitmap \f$ \mathcal{K} \f$ periodic boundary conditions are imposed
- * in all directions, then complex \f$ \mathcal{K} \f$ became n-dimensional torus. One can use various constructors
- * from the file Bitmap_cubical_complex_periodic_boundary_conditions_base.h to construct cubical complex with periodic
- * boundary conditions. One can also use Perseus style input files (see \ref FileFormatsPerseus).
- *
- * \section BitmapExamples Examples
- * End user programs are available in example/Bitmap_cubical_complex and utilities/Bitmap_cubical_complex folders.
- *
- */
-/** @} */ // end defgroup cubical_complex
-
-} // namespace cubical_complex
-
-namespace Cubical_complex = cubical_complex;
-
-} // namespace Gudhi
-
-#endif // DOC_GUDHI_CUBICAL_COMPLEX_COMPLEX_H_
diff --git a/doc/Bitmap_cubical_complex/bitmapAllCubes.png b/doc/Bitmap_cubical_complex/bitmapAllCubes.png
deleted file mode 100644
index 77167b13..00000000
--- a/doc/Bitmap_cubical_complex/bitmapAllCubes.png
+++ /dev/null
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diff --git a/doc/Bitmap_cubical_complex/exampleBitmap.png b/doc/Bitmap_cubical_complex/exampleBitmap.png
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index 069c6eb2..00000000
--- a/doc/Bitmap_cubical_complex/exampleBitmap.png
+++ /dev/null
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diff --git a/doc/Bottleneck_distance/COPYRIGHT b/doc/Bottleneck_distance/COPYRIGHT
deleted file mode 100644
index 1c2016b1..00000000
--- a/doc/Bottleneck_distance/COPYRIGHT
+++ /dev/null
@@ -1,19 +0,0 @@
-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): François Godi
-
-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/Bottleneck_distance/Intro_bottleneck_distance.h b/doc/Bottleneck_distance/Intro_bottleneck_distance.h
deleted file mode 100644
index f8fce96c..00000000
--- a/doc/Bottleneck_distance/Intro_bottleneck_distance.h
+++ /dev/null
@@ -1,51 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author: François Godi
- *
- * 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/>.
- */
-
-#ifndef DOC_BOTTLENECK_DISTANCE_INTRO_BOTTLENECK_DISTANCE_H_
-#define DOC_BOTTLENECK_DISTANCE_INTRO_BOTTLENECK_DISTANCE_H_
-
-// needs namespace for Doxygen to link on classes
-namespace Gudhi {
-// needs namespace for Doxygen to link on classes
-namespace persistence_diagram {
-
-/** \defgroup bottleneck_distance Bottleneck distance
- *
- * \author Fran&ccedil;ois Godi
- * @{
- *
- * \section bottleneckdefinition Definition
- *
- * The bottleneck distance measures the similarity between two persistence diagrams. It is the shortest distance b for
- * which there exists a perfect matching between the points of the two diagrams (completed with all the points on the
- * diagonal in order to ignore cardinality mismatchs) such that any couple of matched points are at distance at most b.
- *
- * \image html perturb_pd.png On this picture, the red edges represent the matching. The bottleneck distance is the length of the longest edge.
- *
- */
-/** @} */ // end defgroup bottleneck_distance
-
-} // namespace persistence_diagram
-
-} // namespace Gudhi
-
-#endif // DOC_BOTTLENECK_DISTANCE_INTRO_BOTTLENECK_DISTANCE_H_
diff --git a/doc/Bottleneck_distance/perturb_pd.png b/doc/Bottleneck_distance/perturb_pd.png
deleted file mode 100644
index be638de0..00000000
--- a/doc/Bottleneck_distance/perturb_pd.png
+++ /dev/null
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diff --git a/doc/Cech_complex/COPYRIGHT b/doc/Cech_complex/COPYRIGHT
deleted file mode 100644
index 5f1d97cc..00000000
--- a/doc/Cech_complex/COPYRIGHT
+++ /dev/null
@@ -1,19 +0,0 @@
-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): Vincent Rouvreau
-
-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/Cech_complex/Intro_cech_complex.h b/doc/Cech_complex/Intro_cech_complex.h
deleted file mode 100644
index 4483bcb9..00000000
--- a/doc/Cech_complex/Intro_cech_complex.h
+++ /dev/null
@@ -1,114 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Vincent Rouvreau
- *
- * Copyright (C) 2018 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/>.
- */
-
-#ifndef DOC_CECH_COMPLEX_INTRO_CECH_COMPLEX_H_
-#define DOC_CECH_COMPLEX_INTRO_CECH_COMPLEX_H_
-
-namespace Gudhi {
-
-namespace cech_complex {
-
-/** \defgroup cech_complex ÄŒech complex
- *
- * \author Vincent Rouvreau
- *
- * @{
- *
- * \section cechdefinition ÄŒech complex definition
- *
- * ÄŒech complex
- * <a target="_blank" href="https://en.wikipedia.org/wiki/%C4%8Cech_cohomology">(Wikipedia)</a> is a
- * <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a> constructed
- * from a proximity graph. The set of all simplices is filtered by the radius of their minimal enclosing ball.
- *
- * The input shall be a point cloud in an Euclidean space.
- *
- * \remark For people only interested in the topology of the \ref cech_complex (for instance persistence),
- * \ref alpha_complex is equivalent to the \ref cech_complex and much smaller if you do not bound the radii.
- * \ref cech_complex can still make sense in higher dimension precisely because you can bound the radii.
- *
- * \subsection cechalgorithm Algorithm
- *
- * Cech_complex first builds a proximity graph from a point cloud.
- * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from
- * `Gudhi::Minimal_enclosing_ball_radius` function.
- *
- * All edges that have a filtration value strictly greater than a user given maximal radius value, \f$max\_radius\f$,
- * are not inserted into the complex.
- *
- * Vertex name correspond to the index of the point in the given range (aka. the point cloud).
- *
- * \image html "cech_one_skeleton.png" "ÄŒech complex proximity graph representation"
- *
- * When creating a simplicial complex from this proximity graph, Cech_complex inserts the proximity graph into the
- * simplicial complex data structure, and then expands the simplicial complex when required.
- *
- * On this example, as edges \f$(x,y)\f$, \f$(y,z)\f$ and \f$(z,y)\f$ are in the complex, the minimal ball radius
- * containing the points \f$(x,y,z)\f$ is computed.
- *
- * \f$(x,y,z)\f$ is inserted to the simplicial complex with the filtration value set with
- * \f$mini\_ball\_radius(x,y,z))\f$ iff \f$mini\_ball\_radius(x,y,z)) \leq max\_radius\f$.
- *
- * And so on for higher dimensions.
- *
- * \image html "cech_complex_representation.png" "ÄŒech complex expansion"
- *
- * The minimal ball radius computation is insured by
- * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html">
- * the miniball software (V3.0)</a> - Smallest Enclosing Balls of Points - and distributed with GUDHI.
- * Please refer to
- * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/texts/own_work/esa99_final.pdf">
- * the miniball software design description</a> for more information about this computation.
- *
- * This radius computation is the reason why the Cech_complex is taking much more time to be computed than the
- * \ref rips_complex but it offers more topological guarantees.
- *
- * If the Cech_complex interfaces are not detailed enough for your need, please refer to
- * <a href="_cech_complex_2cech_complex_step_by_step_8cpp-example.html">
- * cech_complex_step_by_step.cpp</a> example, where the graph construction over the Simplex_tree is more detailed.
- *
- * \subsection cechpointscloudexample Example from a point cloud
- *
- * This example builds the proximity graph from the given points, and maximal radius values.
- * Then it creates a `Simplex_tree` with it.
- *
- * Then, it is asked to display information about the simplicial complex.
- *
- * \include Cech_complex/cech_complex_example_from_points.cpp
- *
- * When launching (maximal enclosing ball radius is 1., is expanded until dimension 2):
- *
- * \code $> ./Cech_complex_example_from_points
- * \endcode
- *
- * the program output is:
- *
- * \include Cech_complex/cech_complex_example_from_points_for_doc.txt
- *
- */
-/** @} */ // end defgroup cech_complex
-
-} // namespace cech_complex
-
-} // namespace Gudhi
-
-#endif // DOC_CECH_COMPLEX_INTRO_CECH_COMPLEX_H_
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diff --git a/doc/Cech_complex/cech_one_skeleton.png b/doc/Cech_complex/cech_one_skeleton.png
deleted file mode 100644
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+++ /dev/null
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diff --git a/doc/Contraction/COPYRIGHT b/doc/Contraction/COPYRIGHT
deleted file mode 100644
index 5b606ac2..00000000
--- a/doc/Contraction/COPYRIGHT
+++ /dev/null
@@ -1,18 +0,0 @@
-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): David Salinas
-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/>.
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diff --git a/doc/Contraction/sphere_contraction_representation.png b/doc/Contraction/sphere_contraction_representation.png
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diff --git a/doc/Nerve_GIC/COPYRIGHT b/doc/Nerve_GIC/COPYRIGHT
deleted file mode 100644
index 6b33053e..00000000
--- a/doc/Nerve_GIC/COPYRIGHT
+++ /dev/null
@@ -1,19 +0,0 @@
-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): Mathieu Carrière
-
-Copyright (C) 2017 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/Nerve_GIC/GIC.jpg b/doc/Nerve_GIC/GIC.jpg
deleted file mode 100644
index cb1b9b7f..00000000
--- a/doc/Nerve_GIC/GIC.jpg
+++ /dev/null
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diff --git a/doc/Nerve_GIC/GIC.pdf b/doc/Nerve_GIC/GIC.pdf
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index 30525745..00000000
--- a/doc/Nerve_GIC/GIC.pdf
+++ /dev/null
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diff --git a/doc/Nerve_GIC/Intro_graph_induced_complex.h b/doc/Nerve_GIC/Intro_graph_induced_complex.h
deleted file mode 100644
index bc8aecc3..00000000
--- a/doc/Nerve_GIC/Intro_graph_induced_complex.h
+++ /dev/null
@@ -1,186 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Mathieu Carriere
- *
- * Copyright (C) 2017 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/>.
- */
-
-#ifndef DOC_COVER_COMPLEX_INTRO_COVER_COMPLEX_H_
-#define DOC_COVER_COMPLEX_INTRO_COVER_COMPLEX_H_
-
-namespace Gudhi {
-
-namespace cover_complex {
-
-/** \defgroup cover_complex Cover complex
- *
- * \author Mathieu Carrière
- *
- * @{
- *
- * Visualizations of the simplicial complexes can be done with either
- * neato (from <a target="_blank" href="http://www.graphviz.org/">graphviz</a>),
- * <a target="_blank" href="http://www.geomview.org/">geomview</a>,
- * <a target="_blank" href="https://github.com/MLWave/kepler-mapper">KeplerMapper</a>.
- * Input point clouds are assumed to be
- * <a target="_blank" href="http://www.geomview.org/docs/html/OFF.html">OFF files</a>.
- *
- * \section covers Covers
- *
- * Nerves and Graph Induced Complexes require a cover C of the input point cloud P,
- * that is a set of subsets of P whose union is P itself.
- * Very often, this cover is obtained from the preimage of a family of intervals covering
- * the image of some scalar-valued function f defined on P. This family is parameterized
- * by its resolution, which can be either the number or the length of the intervals,
- * and its gain, which is the overlap percentage between consecutive intervals (ordered by their first values).
- *
- * \section nerves Nerves
- *
- * \subsection nervedefinition Nerve definition
- *
- * Assume you are given a cover C of your point cloud P. Then, the Nerve of this cover
- * is the simplicial complex that has one k-simplex per k-fold intersection of cover elements.
- * See also <a target="_blank" href="https://en.wikipedia.org/wiki/Nerve_of_a_covering"> Wikipedia </a>.
- *
- * \image html "nerve.png" "Nerve of a double torus"
- *
- * \subsection nerveexample Example
- *
- * This example builds the Nerve of a point cloud sampled on a 3D human shape (human.off).
- * The cover C comes from the preimages of intervals (10 intervals with gain 0.3)
- * covering the height function (coordinate 2),
- * which are then refined into their connected components using the triangulation of the .OFF file.
- *
- * \include Nerve_GIC/Nerve.cpp
- *
- * When launching:
- *
- * \code $> ./Nerve ../../data/points/human.off 2 10 0.3 -v
- * \endcode
- *
- * the program output is:
- *
- * \include Nerve_GIC/Nerve.txt
- *
- * The program also writes a file ../../data/points/human_sc.txt. The first three lines in this file are the location
- * of the input point cloud and the function used to compute the cover.
- * The fourth line contains the number of vertices nv and edges ne of the Nerve.
- * The next nv lines represent the vertices. Each line contains the vertex ID,
- * the number of data points it contains, and their average color function value.
- * Finally, the next ne lines represent the edges, characterized by the ID of their vertices.
- *
- * Using KeplerMapper, one can obtain the following visualization:
- *
- * \image html "nervevisu.jpg" "Visualization with KeplerMapper"
- *
- * \section gic Graph Induced Complexes (GIC)
- *
- * \subsection gicdefinition GIC definition
- *
- * Again, assume you are given a cover C of your point cloud P. Moreover, assume
- * you are also given a graph G built on top of P. Then, for any clique in G
- * whose nodes all belong to different elements of C, the GIC includes a corresponding
- * simplex, whose dimension is the number of nodes in the clique minus one.
- * See \cite Dey13 for more details.
- *
- * \image html "GIC.jpg" "GIC of a point cloud."
- *
- * \subsection gicexamplevor Example with cover from Voronoï
- *
- * This example builds the GIC of a point cloud sampled on a 3D human shape (human.off).
- * We randomly subsampled 100 points in the point cloud, which act as seeds of
- * a geodesic Voronoï diagram. Each cell of the diagram is then an element of C.
- * The graph G (used to compute both the geodesics for Voronoï and the GIC)
- * comes from the triangulation of the human shape. Note that the resulting simplicial complex is in dimension 3
- * in this example.
- *
- * \include Nerve_GIC/VoronoiGIC.cpp
- *
- * When launching:
- *
- * \code $> ./VoronoiGIC ../../data/points/human.off 700 -v
- * \endcode
- *
- * the program outputs SC.off. Using e.g.
- *
- * \code $> geomview ../../data/points/human_sc.off
- * \endcode
- *
- * one can obtain the following visualization:
- *
- * \image html "gicvoronoivisu.jpg" "Visualization with Geomview"
- *
- * \subsection functionalGICdefinition Functional GIC
- *
- * If one restricts to the cliques in G whose nodes all belong to preimages of consecutive
- * intervals (assuming the cover of the height function is minimal, i.e. no more than
- * two intervals can intersect at a time), the GIC is of dimension one, i.e. a graph.
- * We call this graph the functional GIC. See \cite Carriere16 for more details.
- *
- * \subsection functionalGICexample Example
- *
- * Functional GIC comes with automatic selection of the Rips threshold,
- * the resolution and the gain of the function cover. See \cite Carriere17c for more details. In this example,
- * we compute the functional GIC of a Klein bottle embedded in R^5,
- * where the graph G comes from a Rips complex with automatic threshold,
- * and the cover C comes from the preimages of intervals covering the first coordinate,
- * with automatic resolution and gain. Note that automatic threshold, resolution and gain
- * can be computed as well for the Nerve.
- *
- * \include Nerve_GIC/CoordGIC.cpp
- *
- * When launching:
- *
- * \code $> ./CoordGIC ../../data/points/KleinBottle5D.off 0 -v
- * \endcode
- *
- * the program outputs SC.dot. Using e.g.
- *
- * \code $> neato SC.dot -Tpdf -o SC.pdf
- * \endcode
- *
- * one can obtain the following visualization:
- *
- * \image html "coordGICvisu2.jpg" "Visualization with Neato"
- *
- * where nodes are colored by the filter function values and, for each node, the first number is its ID
- * and the second is the number of data points that its contain.
- *
- * We also provide an example on a set of 72 pictures taken around the same object (lucky_cat.off).
- * The function is now the first eigenfunction given by PCA, whose values
- * are written in a file (lucky_cat_PCA1). Threshold, resolution and gain are automatically selected as before.
- *
- * \include Nerve_GIC/FuncGIC.cpp
- *
- * When launching:
- *
- * \code $> ./FuncGIC ../../data/points/COIL_database/lucky_cat.off ../../data/points/COIL_database/lucky_cat_PCA1 -v
- * \endcode
- *
- * the program outputs again SC.dot which gives the following visualization after using neato:
- *
- * \image html "funcGICvisu.jpg" "Visualization with neato"
- *
- */
-/** @} */ // end defgroup cover_complex
-
-} // namespace cover_complex
-
-} // namespace Gudhi
-
-#endif // DOC_COVER_COMPLEX_INTRO_COVER_COMPLEX_H_
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-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Pawel Dlotko
- *
- * Copyright (C) 2016 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/>.
- */
-
-#ifndef DOC_GUDHI_STAT_H_
-#define DOC_GUDHI_STAT_H_
-
-namespace Gudhi {
-
-namespace Persistence_representations {
-
-/** \defgroup Persistence_representations Persistence representations
- *
- * \author Pawel Dlotko
- *
- * @{
- *\section Persistence_representations_idea Idea
-
- In order to perform most of the statistical tests and machine learning algorithms on a data one need to be able to
- perform only a very limited number of operations on them. Let us fix a representation of
- data of a type A. To perform most of the statistical and machine learning operations one need to be able to compute
- average of objects of type A (so that the averaged object is also of a type A), to
- compute distance between objects of a type A, to vectorize object of a type A and to compute scalar product of a pair
- objects of a type A.
-
- To put this statement into a context, let us assume we have two collections \f$ c_1,\ldots,c_n\f$ and
- \f$d_1,...,d_n\f$ of objects of a type A. We want to verify if the average of those two collections
- are different by performing a permutation test.
- First of all, we compute averages of those two collections: C average of \f$ c_1,\ldots,c_n \f$ and D average of
- \f$d_1,\ldots,d_n\f$. Note that both C and D are of a type A. Then we compute \f$d(C,D)\f$,
- a distance between C and D.
- Later we put the two collections into one bin:
- \f[B = \{ c_1,...,c_n,d_1,...,d_n \}\f]
- Then we shuffle B, and we divide the shuffled version of B into two classes: \f$B_1\f$ and \f$B_2\f$ (in this case, of
- the same cardinality). Then we compute averages \f$\hat{B_1}\f$ and \f$\hat{B_2}\f$
- of elements in \f$B_1\f$ and \f$B_2\f$. Note that again, \f$\hat{B_1}\f$ and \f$\hat{B_2}\f$ are of a type A.
- Then we compute their distance \f$d(\hat{B_1},\hat{B_2})\f$. The procedure of shuffling and dividing the set \f$B\f$
- is repeated \f$N\f$ times (where \f$N\f$ is reasonably large number).
- Then the p-value of a statement that the averages of \f$c_1,...,c_n\f$ and \f$d_1,...,d_n\f$ is approximated by the
- number of times \f$d(\hat{B_1},\hat{B_2}) > d(C,D)\f$ divided by \f$N\f$.
-
- The permutation test reminded above can be performed for any type A which can be averaged, and which allows for
- computations of distances.
-
- The Persistence\_representations contains a collection of various representations of persistent homology that
- implements various concepts described below:
-
- \li Concept of a representation of persistence that allows averaging (so that the average object is of the same type).
- \li Concept of representation of persistence that allows computations of distances.
- \li Concept of representation of persistence that allows computations of scalar products.
- \li Concept of representation of persistence that allows vectorization.
- \li Concept of representation of persistence that allows computations of real-valued characteristics of objects.
-
-
- At the moment an implementation of the following representations of persistence are available (further details of
- those representations will be discussed later):
-
- \li Exact persistence landscapes (allow averaging, computation of distances, scalar products, vectorizations and real
- value characteristics).
- \li Persistence landscapes on a grid (allow averaging, computation of distances scalar products, vectorizations and
- real value characteristics).
- \li Persistence heat maps – various representations where one put some weighted or not Gaussian kernel for each point
- of diagram (allow averaging, computation of distances, scalar products,
- vectorizations and real value characteristics).
- \li Persistence vectors (allow averaging, computation of distances, scalar products, vectorizations and real value
- characteristics).
- \li Persistence diagrams / barcodes (allow computation of distances, vectorizations and real value characteristics).
-
-
- Note that at the while functionalities like averaging, distances and scalar products are fixed, there is no canonical
- way of vectorizing and computing real valued characteristics of objects. Therefore the
- vectorizations and computation of real value characteristics procedures are quite likely to evolve in the furthering
- versions of the library.
-
- The main aim of this implementation is to be able to implement various statistical methods, both on the level of C++
- and on the level of python. The methods will operate on the functionalities offered
- by concepts. That means that the statistical and ML methods will be able to operate on any representation that
- implement the required concept (including the ones that are not in the library at the moment).
- That gives provides a framework, that is very easy to extend, for topological statistics.
-
- Below we are discussing the representations which are currently implemented in Persistence\_representations package:
-
- \section sec_persistence_landscapes Persistence Landscapes
- <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Persistence_landscape <br>
- Persistence landscapes were originally proposed by Bubenik in \cite bubenik_landscapes_2015. Efficient algorithms to
- compute them rigorously were proposed by Bubenik and Dlotko in \cite bubenik_dlotko_landscapes_2016. The idea of
- persistence landscapes is shortly summarized in below.
-
- To begin with, suppose we are given a point \f$(b,d) \in \mathbb{R}^2\f$ in a
- persistence diagram. With this point, we associate a piecewise
- linear function \f$f_{(b,d)} : \mathbb{R} \rightarrow [0,\infty)\f$, which is
- defined as
-
- \f[f_{(b,d)}(x) =
- \left\{ \begin{array}{ccl}
- 0 & \mbox{ if } & x \not\in (b, d) \; , \\
- x - b & \mbox{ if } & x \in \left( b, \frac{b+d}{2}
- \right] \; , \\
- d - x & \mbox{ if } & x \in \left(\frac{b+d}{2},
- d \right) \; .
- \end{array} \right.
- \f]
-
- A persistence landscape of the birth-death
- pairs \f$(b_i , d_i)\f$, where \f$i = 1,\ldots,m\f$, which constitute the given
- persistence diagram is the sequence of functions \f$\lambda_k : \mathbb{R} \rightarrow [0,\infty)\f$ for \f$k \in
- \mathbb{N}\f$, where \f$\lambda_k(x)\f$
- denotes the \f$k^{\rm th}\f$ largest value of the numbers \f$f_{(b_i,d_i)}(x)\f$,
- for \f$i = 1, \ldots, m\f$, and we define \f$\lambda_k(x) = 0\f$ if \f$k > m\f$.
- Equivalently, this sequence of functions can be combined into a single
- function \f$L : \mathbb{N} \times \mathbb{R} \to [0,\infty)\f$ of two
- variables, if we define \f$L(k,t) = \lambda_k(t)\f$.
-
- The detailed description of algorithms used to compute persistence landscapes can be found in
- \cite bubenik_dlotko_landscapes_2016.
- Note that this implementation provides exact representation of landscapes. That have many advantages, but also a few
- drawbacks. For instance, as discussed
- in \cite bubenik_dlotko_landscapes_2016, the exact representation of landscape may be of quadratic size with respect
- to the input persistence diagram. It may therefore happen
- that, for very large diagrams, using this representation may be memory--prohibitive. In such a case, there are two
- possible ways to proceed:
-
- \li Use non exact representation on a grid described in the Section \ref sec_landscapes_on_grid.
- \li Compute just a number of initial nonzero landscapes. This option is available from C++ level as a last parameter of
- the constructor of persistence landscape (set by default to std::numeric_limits<size_t>::max()).
-
-
-
- \section sec_landscapes_on_grid Persistence Landscapes on a grid
- <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Persistence_landscape_on_grid <br>
- This is an alternative, not--exact, representation of persistence landscapes defined in the Section \ref
- sec_persistence_landscapes. Unlike in the Section \ref sec_persistence_landscapes we build a
- representation of persistence landscape by sampling its values on a finite, equally distributed grid of points.
- Since, the persistence landscapes that originate from persistence diagrams have slope \f$1\f$ or \f$-1\f$, we have an
- estimate of a region between the grid points where the landscape cab be located.
- That allows to estimate an error make when performing various operations on landscape. Note that for average
- landscapes the slope is in range \f$[-1,1]\f$ and similar estimate can be used.
-
- Due to a lack of rigorous description of the algorithms to deal with this non--rigorous representation of persistence
- landscapes in the literature, we are providing a short discussion of them in below.
-
- Let us assume that we want to compute persistence landscape on a interval \f$[x,y]\f$. Let us assume that we want to
- use \f$N\f$ grid points for that purpose.
- Then we will sample the persistence landscape on points \f$x_1 = x , x_2 = x + \frac{y-x}{N}, \ldots , x_{N} = y\f$.
- Persistence landscapes are represented as a vector of
- vectors of real numbers. Assume that i-th vector consist of \f$n_i\f$ numbers sorted from larger to smaller. They
- represent the values of the functions
- \f$\lambda_1,\ldots,\lambda_{n_i}\f$ ,\f$\lambda_{n_i+1}\f$ and the functions with larger indices are then zero
- functions) on the i-th point of a grid, i.e. \f$x + i \frac{y-x}{N}\f$.
-
- When averaging two persistence landscapes represented by a grid we need to make sure that they are defined in a
- compatible grids. I.e. the intervals \f$[x,y]\f$ on which they are defined are
- the same, and the numbers of grid points \f$N\f$ are the same in both cases. If this is the case, we simply compute
- point-wise averages of the entries of corresponding
- vectors (In this whole section we assume that if one vector of numbers is shorter than another, we extend the shorter
- one with zeros so that they have the same length.)
-
- Computations of distances between two persistence landscapes on a grid is not much different than in the rigorous
- case. In this case, we sum up the distances between the same levels of
- corresponding landscapes. For fixed level, we approximate the landscapes between the corresponding constitutive
- points of landscapes by linear functions, and compute the \f$L^p\f$ distance between them.
-
- Similarly as in case of distance, when computing the scalar product of two persistence landscapes on a grid, we sum up
- the scalar products of corresponding levels of landscapes. For each level,
- we assume that the persistence landscape on a grid between two grid points is approximated by linear function.
- Therefore to compute scalar product of two corresponding levels of landscapes,
- we sum up the integrals of products of line segments for every pair of constitutive grid points.
-
- Note that for this representation we need to specify a few parameters:
-
- \li Begin and end point of a grid -- the interval \f$[x,y]\f$ (real numbers).
- \li Number of points in a grid (positive integer \f$N\f$).
-
-
- Note that the same representation is used in TDA R-package \cite Fasy_Kim_Lecci_Maria_tda.
-
- \section sec_persistence_heat_maps Persistence heat maps
- <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Persistence_heat_maps <br>
- This is a general class of discrete structures which are based on idea of placing a kernel in the points of
- persistence diagrams.
- This idea appeared in work by many authors over the last 15 years. As far as we know this idea was firstly described
- in the work of Bologna group in \cite Ferri_Frosini_comparision_sheme_1 and \cite Ferri_Frosini_comparision_sheme_2.
- Later it has been described by Colorado State University group in \cite Persistence_Images_2017. The presented paper
- in the first time provide a discussion of stability of the representation.
- Also, the same ideas are used in construction of two recent kernels used for machine learning:
- \cite Kusano_Fukumizu_Hiraoka_PWGK and \cite Reininghaus_Huber_ALL_PSSK. Both the kernel's construction uses
- interesting ideas to ensure stability of the representation with respect to Wasserstein metric. In the kernel
- presented in \cite Kusano_Fukumizu_Hiraoka_PWGK, a scaling function is used to multiply the Gaussian kernel in the
- way that the points close to diagonal got low weight and consequently do not have a big influence on the resulting
- distribution. In \cite Reininghaus_Huber_ALL_PSSK for every point \f$(b,d)\f$ two Gaussian kernels
- are added: first, with a weight 1 in a point \f$(b,d)\f$, and the second, with the weight -1 for a point \f$(b,d)\f$.
- In both cases, the representations are stable with respect to 1-Wasserstein distance.
-
- In Persistence\_representations package we currently implement a discretization of the distributions described above.
- The base of this implementation is 2-dimensional array of pixels. Each pixel have assigned a real value which
- is a sum of values of distributions induced by each point of the persistence diagram. At the moment we compute the
- sum of values on a center of a pixels. It can be easily extended to any other function
- (like for instance sum of integrals of the intermediate distribution on a pixel).
-
- The parameters that determine the structure are the following:
-
- \li A positive integer k determining the size of the kernel we used (we always assume that the kernels are square).
- \li A filter: in practice a square matrix of a size \f$2k+1 \times 2k+1\f$. By default, this is a discretization of
- N(0,1) kernel.
- \li The box \f$[x_0,x_1]\times [y_0,y_1]\f$ bounding the domain of the persistence image.
- \li Scaling function. Each Gaussian kernel at point \f$(p,q)\f$ gets multiplied by the value of this function at the
- point \f$(p,q)\f$.
- \li A boolean value determining if the space below diagonal should be erased or not. To be precise: when points close
- to diagonal are given then sometimes the kernel have support that reaches the region
- below the diagonal. If the value of this parameter is true, then the values below diagonal can be erased.
-
-
- \section sec_persistence_vectors Persistence vectors
- <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Vector_distances_in_diagram <br>
- This is a representation of persistent homology in a form of a vector which was designed for an application in 3d
- graphic in \cite Carriere_Oudot_Ovsjanikov_top_signatures_3d. Below we provide a short description of this
- representation.
-
- Given a persistence diagram \f$D = \{ (b_i,d_i) \}\f$, for every pair of birth--death points \f$(b_1,d_1)\f$ and
- \f$(b_2,d_2)\f$ we compute the following three distances:
-
- \li \f$d( (b_1,d_1) , (b_2,d_2) )\f$.
- \li \f$d( (b_1,d_1) , (\frac{b_1,d_1}{2},\frac{b_1,d_1}{2}) )\f$.
- \li \f$d( (b_2,d_2) , (\frac{b_2,d_2}{2},\frac{b_2,d_2}{2}) )\f$.
-
- We pick the smallest of those and add it to a vector. The obtained vector of numbers is then sorted in decreasing
- order. This way we obtain a persistence vector representing the diagram.
-
- Given two persistence vectors, the computation of distances, averages and scalar products is straightforward. Average
- is simply a coordinate-wise average of a collection of vectors. In this section we
- assume that the vectors are extended by zeros if they are of a different size. To compute distances we compute
- absolute value of differences between coordinates. A scalar product is a sum of products of
- values at the corresponding positions of two vectors.
-
- */
-/** @} */ // end defgroup Persistence_representations
-
-} // namespace Persistence_representations
-} // namespace Gudhi
-
-#endif // Persistence_representations
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diff --git a/doc/Persistent_cohomology/COPYRIGHT b/doc/Persistent_cohomology/COPYRIGHT
deleted file mode 100644
index 6cde9520..00000000
--- a/doc/Persistent_cohomology/COPYRIGHT
+++ /dev/null
@@ -1,19 +0,0 @@
-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): Clément Maria
-
-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/Persistent_cohomology/Intro_persistent_cohomology.h b/doc/Persistent_cohomology/Intro_persistent_cohomology.h
deleted file mode 100644
index 5fb9d4d2..00000000
--- a/doc/Persistent_cohomology/Intro_persistent_cohomology.h
+++ /dev/null
@@ -1,270 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Clément Maria
- *
- * Copyright (C) 2014 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/>.
- */
-
-#ifndef DOC_PERSISTENT_COHOMOLOGY_INTRO_PERSISTENT_COHOMOLOGY_H_
-#define DOC_PERSISTENT_COHOMOLOGY_INTRO_PERSISTENT_COHOMOLOGY_H_
-
-// needs namespace for Doxygen to link on classes
-namespace Gudhi {
-// needs namespace for Doxygen to link on classes
-namespace persistent_cohomology {
-
-/** \defgroup persistent_cohomology Persistent Cohomology
-
- \author Clément Maria
-
- Computation of persistent cohomology using the algorithm of
- \cite DBLP:journals/dcg/SilvaMV11 and \cite DBLP:journals/corr/abs-1208-5018
- and the Compressed Annotation Matrix
- implementation of \cite DBLP:conf/esa/BoissonnatDM13
-
- The theory of homology consists in attaching to a topological space a sequence of
- (homology) groups,
- capturing global topological features
- like connected components, holes, cavities, etc. Persistent homology studies the evolution
- -- birth, life and death -- of
- these features when the topological space is changing. Consequently, the theory is essentially
- composed of three elements:
- topological spaces, their homology groups and an evolution scheme.
-
- \section persistencetopolocalspaces Topological Spaces
- Topological spaces are represented by simplicial complexes.
- Let \f$V = \{1, \cdots ,|V|\}\f$ be a set of <EM>vertices</EM>.
- A <EM>simplex</EM> \f$\sigma\f$ is a subset of vertices
- \f$\sigma \subseteq V\f$. A <EM>simplicial complex</EM> \f$\mathbf{K}\f$
- on \f$V\f$ is a collection of simplices \f$\{\sigma\}\f$,
- \f$\sigma \subseteq V\f$, such that \f$\tau \subseteq \sigma \in \mathbf{K}
- \Rightarrow \tau \in \mathbf{K}\f$. The dimension \f$n=|\sigma|-1\f$ of \f$\sigma\f$
- is its number of elements minus 1. A <EM>filtration</EM> of a simplicial complex is
- a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying \f$f(\tau)\leq
- f(\sigma)\f$ whenever \f$\tau \subseteq \sigma\f$.
-
- We define the concept FilteredComplex which enumerates the requirements for a class
- to represent a filtered complex from which persistent homology may be computed.
- We use the vocabulary of simplicial complexes, but the concept
- is valid for any type of cell complex. The main requirements
- are the definition of:
- \li type <CODE>Indexing_tag</CODE>, which is a model of the concept
- <CODE>IndexingTag</CODE>,
- describing the nature of the indexing scheme,
- \li type Simplex_handle to manipulate simplices,
- \li method <CODE>int dimension(Simplex_handle)</CODE> returning
- the dimension of a simplex,
- \li type and method <CODE>Boundary_simplex_range
- boundary_simplex_range(Simplex_handle)</CODE> that returns
- a range giving access to the codimension 1 subsimplices of the
- input simplex, as-well-as the coefficients \f$(-1)^i\f$ in the
- definition of the operator \f$\partial\f$. The iterators have
- value type <CODE>Simplex_handle</CODE>,
- \li type and method
- <CODE>Filtration_simplex_range filtration_simplex_range ()</CODE>
- that returns a range giving
- access to all the simplices of the complex read in the order
- assigned by the indexing scheme,
- \li type and method
- <CODE>Filtration_value filtration (Simplex_handle)</CODE> that returns the value of
- the filtration on the simplex represented by the handle.
-
- \section persistencehomology Homology
- For a ring \f$\mathcal{R}\f$, the group of <EM>n-chains</EM>,
- denoted \f$\mathbf{C}_n(\mathbf{K},\mathcal{R})\f$, of \f$\mathbf{K}\f$ is the
- group of formal sums of
- n-simplices with \f$\mathcal{R}\f$ coefficients. The <EM>boundary operator</EM> is a
- linear operator
- \f$\partial_n: \mathbf{C}_n(\mathbf{K},\mathcal{R}) \rightarrow \mathbf{C}_{n-1}(\mathbf{K},\mathcal{R})\f$
- such that \f$\partial_n \sigma = \partial_n [v_0, \cdots , v_n] =
- \sum_{i=0}^n (-1)^{i}[v_0,\cdots ,\widehat{v_i}, \cdots,v_n]\f$,
- where \f$\widehat{v_i}\f$ means \f$v_i\f$ is omitted from the list. The chain
- groups form a sequence:
-
- \f[\cdots \ \ \mathbf{C}_n(\mathbf{K},\mathcal{R}) \xrightarrow{\ \partial_n\ } \mathbf{C}_{n-1}(\mathbf{K},\mathcal{R})
- \xrightarrow{\partial_{n-1}} \cdots \xrightarrow{\ \partial_2 \ }
- \mathbf{C}_1(\mathbf{K},\mathcal{R}) \xrightarrow{\ \partial_1 \ } \mathbf{C}_0(\mathbf{K},\mathcal{R}) \f]
-
- of finitely many groups \f$\mathbf{C}_n(\mathbf{K},\mathcal{R})\f$ and homomorphisms
- \f$\partial_n\f$, indexed by the dimension \f$n \geq 0\f$.
- The boundary operators satisfy the property \f$\partial_n \circ \partial_{n+1}=0\f$
- for every \f$n > 0\f$
- and we define the homology groups:
-
- \f[\mathbf{H}_n(\mathbf{K},\mathcal{R}) = \ker \partial_n / \mathrm{im} \ \partial_{n+1}\f]
-
- We refer to \cite Munkres-elementsalgtop1984 for an introduction to homology
- theory and to \cite DBLP:books/daglib/0025666 for an introduction to persistent homology.
-
- \section persistenceindexingscheme Indexing Scheme
- "Changing" a simplicial complex consists in applying a simplicial map.
- An <EM>indexing scheme</EM> is a directed graph together with a traversal
- order, such that two
- consecutive nodes in the graph are connected by an arrow (either forward or backward).
- The nodes represent simplicial complexes and the directed edges simplicial maps.
-
- From the computational point of view, there are two types of indexing schemes of
- interest
- in persistent homology: <EM>linear</EM> ones
- \f$\bullet \longrightarrow \bullet \longrightarrow \cdots \longrightarrow \bullet
- \longrightarrow \bullet\f$
- in persistent homology \cite DBLP:journals/dcg/ZomorodianC05 ,
- and <EM>zigzag</EM> ones
- \f$\bullet \longrightarrow \bullet \longleftarrow \cdots
- \longrightarrow \bullet
- \longleftarrow \bullet \f$ in zigzag persistent
- homology \cite DBLP:journals/focm/CarlssonS10.
- These indexing schemes have a natural left-to-right traversal order, and we
- describe them with ranges and iterators.
- In the current release of the Gudhi library, only the linear case is implemented.
-
- In the following, we consider the case where the indexing scheme is induced
- by a filtration.
- Ordering the simplices
- by increasing filtration values (breaking ties so as a simplex appears after
- its subsimplices of same filtration value) provides an indexing scheme.
-
-\section pcohexamples Examples
-
-We provide several example files: run these examples with -h for details on their use, and read the README file.
-
-\li <a href="_rips_complex_2rips_persistence_8cpp-example.html">
-Rips_complex/rips_persistence.cpp</a> computes the Rips complex of a point cloud and outputs its persistence
-diagram.
-\code $> ./rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3 \endcode
-\code The complex contains 177838 simplices
- and has dimension 3
-3 0 0 inf
-3 1 0.0983494 inf
-3 1 0.104347 inf
-3 2 0.138335 inf \endcode
-
-\li <a href="_persistent_cohomology_2rips_multifield_persistence_8cpp-example.html">
-Persistent_cohomology/rips_multifield_persistence.cpp</a> computes the Rips complex of a point cloud and outputs its
-persistence diagram with a family of field coefficients.
-
-\li <a href="_rips_complex_2rips_distance_matrix_persistence_8cpp-example.html">
-Rips_complex/rips_distance_matrix_persistence.cpp</a> computes the Rips complex of a distance matrix and
-outputs its persistence diagram.
-
-The file should contain square or lower triangular distance matrix with semicolons as separators.
-The code do not check if it is dealing with a distance matrix. It is the user responsibility to provide a valid input.
-Please refer to data/distance_matrix/lower_triangular_distance_matrix.csv for an example of a file.
-
-\li <a href="_rips_complex_2rips_correlation_matrix_persistence_8cpp-example.html">
-Rips_complex/rips_correlation_matrix_persistence.cpp</a>
-computes the Rips complex of a correlation matrix and outputs its persistence diagram.
-
-Note that no check is performed if the matrix given as the input is a correlation matrix.
-It is the user responsibility to ensure that this is the case. The input is to be given either as a square or a lower
-triangular matrix.
-Please refer to data/correlation_matrix/lower_triangular_correlation_matrix.csv for an example of a file.
-
-\li <a href="_alpha_complex_2alpha_complex_3d_persistence_8cpp-example.html">
-Alpha_complex/alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
-\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file.
-\code $> ./alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45 \endcode
-\code Simplex_tree dim: 3
-2 0 0 inf
-2 1 0.0682162 1.0001
-2 1 0.0934117 1.00003
-2 2 0.56444 1.03938 \endcode
-
-\li <a href="_alpha_complex_2exact_alpha_complex_3d_persistence_8cpp-example.html">
-Alpha_complex/exact_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
-\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file.
-Here, as CGAL computes the exact values, it is slower, but it is necessary when points are on a grid
-for instance.
-\code $> ./exact_alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off -p 2 -m 0.1 \endcode
-\code Simplex_tree dim: 3
-2 0 0 inf
-2 2 0.0002 0.2028 \endcode
-
-\li <a href="_alpha_complex_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
-Alpha_complex/weighted_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
-\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the weighted alpha complex on points sampling from an OFF file
-and a weights file.
-\code $> ./weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off
-../../data/points/tore3D_300.weights -p 2 -m 0.45 \endcode
-\code Simplex_tree dim: 3
-2 0 -1 inf
-2 1 -0.931784 0.000103311
-2 1 -0.906588 2.60165e-05
-2 2 -0.43556 0.0393798 \endcode
-
-\li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html">
-Alpha_complex/alpha_complex_persistence.cpp</a> computes the persistent homology with
-\f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file.
-\code $> ./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off \endcode
-\code Alpha complex is of dimension 3 - 9273 simplices - 300 vertices.
-Simplex_tree dim: 3
-2 0 0 inf
-2 1 0.0682162 1.0001
-2 1 0.0934117 1.00003
-2 2 0.56444 1.03938 \endcode
-
-\li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
-Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
-\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the periodic alpha complex on points sampling from an OFF file.
-The second parameter is a \ref FileFormatsIsoCuboid file with coordinates of the periodic cuboid.
-Note that the lengths of the sides of the periodic cuboid have to be the same.
-\code $> ./periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off
-../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0 \endcode
-\code Periodic Delaunay computed.
-Simplex_tree dim: 3
-3 0 0 inf
-3 1 0.0025 inf
-3 1 0.0025 inf
-3 1 0.0025 inf
-3 2 0.005 inf
-3 2 0.005 inf
-3 2 0.005 inf
-3 3 0.0075 inf \endcode
-
-\li <a href="_persistent_cohomology_2weighted_periodic_alpha_complex_3d_persistence_8cpp-example.html">
-Persistent_cohomology/weighted_periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
-\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the periodic alpha complex on weighted points from an OFF file. The
-additional parameters of this program are:<br>
-(a) The file with the weights of points. The file consist of a sequence of numbers (as many as points).
-Note that the weight of each single point have to be bounded by 1/64 times the square of the cuboid edge length.<br>
-(b) A \ref FileFormatsIsoCuboid file with coordinates of the periodic cuboid.
-Note that the lengths of the sides of the periodic cuboid have to be the same.<br>
-\code $> ./weighted_periodic_alpha_complex_3d_persistence ../../data/points/shifted_sphere.off
-../../data/points/shifted_sphere.weights ../../data/points/iso_cuboid_3_in_0_10.txt 3 1.0 \endcode
-\code Weighted Periodic Delaunay computed.
-Simplex_tree dim: 3
-3 0 -0.0001 inf
-3 1 16.0264 inf
-3 1 16.0273 inf
-3 1 16.0303 inf
-3 2 36.8635 inf
-3 2 36.8704 inf
-3 2 36.8838 inf
-3 3 58.6783 inf \endcode
-
-\li <a href="_persistent_cohomology_2plain_homology_8cpp-example.html">
-Persistent_cohomology/plain_homology.cpp</a> computes the plain homology of a simple simplicial complex without
-filtration values.
-
- */
-
-} // namespace persistent_cohomology
-
-} // namespace Gudhi
-
-#endif // DOC_PERSISTENT_COHOMOLOGY_INTRO_PERSISTENT_COHOMOLOGY_H_
diff --git a/doc/Rips_complex/COPYRIGHT b/doc/Rips_complex/COPYRIGHT
deleted file mode 100644
index 2c31a0d6..00000000
--- a/doc/Rips_complex/COPYRIGHT
+++ /dev/null
@@ -1,19 +0,0 @@
-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): Clément Maria, Pawel Dlotko, Vincent Rouvreau
-
-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/Rips_complex/Intro_rips_complex.h b/doc/Rips_complex/Intro_rips_complex.h
deleted file mode 100644
index 712d3b6e..00000000
--- a/doc/Rips_complex/Intro_rips_complex.h
+++ /dev/null
@@ -1,243 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Clément Maria, Pawel Dlotko, Vincent Rouvreau
- *
- * Copyright (C) 2016 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/>.
- */
-
-#ifndef DOC_RIPS_COMPLEX_INTRO_RIPS_COMPLEX_H_
-#define DOC_RIPS_COMPLEX_INTRO_RIPS_COMPLEX_H_
-
-namespace Gudhi {
-
-namespace rips_complex {
-
-/** \defgroup rips_complex Rips complex
- *
- * \author Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse
- *
- * @{
- *
- * \section ripsdefinition Rips complex definition
- *
- * The Vietoris-Rips complex
- * <a target="_blank" href="https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex">(Wikipedia)</a>
- * is an abstract simplicial complex
- * defined on a finite metric space, where each simplex corresponds to a subset
- * of point whose diameter is smaller that some given threshold.
- * Varying the threshold, we can also see the Rips complex as a filtration of
- * the \f$(n-1)-\f$dimensional simplex, where the filtration value of each
- * simplex is the diameter of the corresponding subset of points.
- *
- * This filtered complex is most often used as an approximation of the
- * ÄŒech complex. After rescaling (Rips using the length of the edges and ÄŒech
- * the half-length), they share the same 1-skeleton and are multiplicatively
- * 2-interleaved or better. While it is slightly bigger, it is also much
- * easier to compute.
- *
- * The number of simplices in the full Rips complex is exponential in the
- * number of vertices, it is thus usually restricted, by excluding all the
- * simplices with filtration value larger than some threshold, and keeping only
- * the dim_max-skeleton.
- *
- * In order to build this complex, the algorithm first builds the graph.
- * The filtration value of each edge is computed from a user-given distance
- * function, or directly read from the distance matrix.
- * In a second step, this graph is inserted in a simplicial complex, which then
- * gets expanded to a flag complex.
- *
- * The input can be given as a range of points and a distance function, or as a
- * distance matrix.
- *
- * Vertex name correspond to the index of the point in the given range (aka. the point cloud).
- *
- * \image html "rips_complex_representation.png" "Rips-complex one skeleton graph representation"
- *
- * On this example, as edges (4,5), (4,6) and (5,6) are in the complex, simplex (4,5,6) is added with the filtration
- * value set with \f$max(filtration(4,5), filtration(4,6), filtration(5,6))\f$.
- * And so on for simplex (0,1,2,3).
- *
- * If the Rips_complex interfaces are not detailed enough for your need, please refer to
- * <a href="_persistent_cohomology_2rips_persistence_step_by_step_8cpp-example.html">
- * rips_persistence_step_by_step.cpp</a> example, where the constructions of the graph and
- * the Simplex_tree are more detailed.
- *
- * \section sparserips Sparse Rips complex
- *
- * Even truncated in filtration value and dimension, the Rips complex remains
- * quite large. However, it is possible to approximate it by a much smaller
- * filtered simplicial complex (linear size, with constants that depend on
- * &epsilon; and the doubling dimension of the space) that is
- * \f$(1+O(\epsilon))-\f$interleaved with it (in particular, their persistence
- * diagrams are at log-bottleneck distance at most \f$O(\epsilon)\f$).
- *
- * The sparse Rips filtration was introduced by Don Sheehy
- * \cite sheehy13linear. We are using the version described in
- * \cite buchet16efficient (except that we multiply all filtration values
- * by 2, to match the usual Rips complex), which proves a
- * \f$\frac{1+\epsilon}{1-\epsilon}\f$-interleaving, although in practice the
- * error is usually smaller.
- * A more intuitive presentation of the idea is available in
- * \cite cavanna15geometric, and in a video \cite cavanna15visualizing.
- *
- * The interface of `Sparse_rips_complex` is similar to the one for the usual
- * `Rips_complex`, except that one has to specify the approximation factor, and
- * there is no option to limit the maximum filtration value (the way the
- * approximation is done means that larger filtration values are much cheaper
- * to handle than low filtration values, so the gain would be too small).
- *
- * Theoretical guarantees are only available for \f$\epsilon<1\f$. The
- * construction accepts larger values of &epsilon;, and the size of the complex
- * keeps decreasing, but there is no guarantee on the quality of the result.
- *
- * \section ripspointsdistance Point cloud and distance function
- *
- * \subsection ripspointscloudexample Example from a point cloud and a distance function
- *
- * This example builds the one skeleton graph from the given points, threshold value, and distance function.
- * Then it creates a `Simplex_tree` with it.
- *
- * Then, it is asked to display information about the simplicial complex.
- *
- * \include Rips_complex/example_one_skeleton_rips_from_points.cpp
- *
- * When launching (Rips maximal distance between 2 points is 12.0, is expanded until dimension 1 - one skeleton graph
- * in other words):
- *
- * \code $> ./Rips_complex_example_one_skeleton_from_points
- * \endcode
- *
- * the program output is:
- *
- * \include Rips_complex/one_skeleton_rips_for_doc.txt
- *
- * \subsection ripsoffexample Example from OFF file
- *
- * This example builds the Rips_complex from the given points in an OFF file, threshold value, and distance
- * function.
- * Then it creates a `Simplex_tree` with it.
- *
- *
- * Then, it is asked to display information about the Rips complex.
- *
- * \include Rips_complex/example_rips_complex_from_off_file.cpp
- *
- * When launching:
- *
- * \code $> ./Rips_complex_example_from_off ../../data/points/alphacomplexdoc.off 12.0 3
- * \endcode
- *
- * the program output is:
- *
- * \include Rips_complex/full_skeleton_rips_for_doc.txt
- *
- *
- * \subsection sparseripspointscloudexample Example of a sparse Rips from a point cloud
- *
- * This example builds the full sparse Rips of a set of 2D Euclidean points, then prints some minimal
- * information about the complex.
- *
- * \include Rips_complex/example_sparse_rips.cpp
- *
- * When launching:
- *
- * \code $> ./Rips_complex_example_sparse
- * \endcode
- *
- * the program output may be (the exact output varies from one run to the next):
- *
- * \code Sparse Rips complex is of dimension 2 - 19 simplices - 7 vertices.
- * \endcode
- *
- *
- *
- * \section ripsdistancematrix Distance matrix
- *
- * \subsection ripsdistancematrixexample Example from a distance matrix
- *
- * This example builds the one skeleton graph from the given distance matrix and threshold value.
- * Then it creates a `Simplex_tree` with it.
- *
- * Then, it is asked to display information about the simplicial complex.
- *
- * \include Rips_complex/example_one_skeleton_rips_from_distance_matrix.cpp
- *
- * When launching (Rips maximal distance between 2 points is 1.0, is expanded until dimension 1 - one skeleton graph
- * with other words):
- *
- * \code $> ./Rips_complex_example_one_skeleton_from_distance_matrix
- * \endcode
- *
- * the program output is:
- *
- * \include Rips_complex/one_skeleton_rips_for_doc.txt
- *
- * \subsection ripscsvdistanceexample Example from a distance matrix read in a csv file
- *
- * This example builds the one skeleton graph from the given distance matrix read in a csv file and threshold value.
- * Then it creates a `Simplex_tree` with it.
- *
- *
- * Then, it is asked to display information about the Rips complex.
- *
- * \include Rips_complex/example_rips_complex_from_csv_distance_matrix_file.cpp
- *
- * When launching:
- *
- * \code $> ./Rips_complex_example_from_csv_distance_matrix ../../data/distance_matrix/full_square_distance_matrix.csv 1.0 3
- * \endcode
- *
- * the program output is:
- *
- * \include Rips_complex/full_skeleton_rips_for_doc.txt
- *
- *
- * \section ripscorrelationematrix Correlation matrix
- *
- * Analogously to the case of distance matrix, Rips complexes can be also constructed based on correlation matrix.
- * Given a correlation matrix M, comportment-wise 1-M is a distance matrix.
- * This example builds the one skeleton graph from the given corelation matrix and threshold value.
- * Then it creates a `Simplex_tree` with it.
- *
- * Then, it is asked to display information about the simplicial complex.
- *
- * \include Rips_complex/example_one_skeleton_rips_from_correlation_matrix.cpp
- *
- * When launching:
- *
- * \code $> ./example_one_skeleton_from_correlation_matrix
- * \endcode
- *
- * the program output is:
- *
- * \include Rips_complex/one_skeleton_rips_from_correlation_matrix_for_doc.txt
- *
- * All the other constructions discussed for Rips complex for distance matrix can be also performed for Rips complexes
- * construction from correlation matrices.
- *
- * @warning As persistence diagrams points will be under the diagonal, bottleneck distance and persistence graphical
- * tool will not work properly, this is a known issue.
- *
- */
-/** @} */ // end defgroup rips_complex
-
-} // namespace rips_complex
-
-} // namespace Gudhi
-
-#endif // DOC_RIPS_COMPLEX_INTRO_RIPS_COMPLEX_H_
diff --git a/doc/Rips_complex/rips_complex_representation.ipe b/doc/Rips_complex/rips_complex_representation.ipe
deleted file mode 100644
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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): Clément Maria
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-Copyright (C) 2015 Inria
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-This program is free software: you can redistribute it and/or modify it under
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-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/Simplex_tree/Intro_simplex_tree.h b/doc/Simplex_tree/Intro_simplex_tree.h
deleted file mode 100644
index db399489..00000000
--- a/doc/Simplex_tree/Intro_simplex_tree.h
+++ /dev/null
@@ -1,87 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Clément Maria
- *
- * Copyright (C) 2014 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/>.
- */
-
-#ifndef DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_
-#define DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_
-
-// needs namespace for Doxygen to link on classes
-namespace Gudhi {
-
-
-/** \defgroup simplex_tree Filtered Complexes
- * @{
- * \author Cl&eacute;ment Maria
- *
- * A simplicial complex \f$\mathbf{K}\f$ on a set of vertices \f$V = \{1, \cdots ,|V|\}\f$ is a collection of
- * simplices \f$\{\sigma\}\f$, \f$\sigma \subseteq V\f$ such that
- * \f$\tau \subseteq \sigma \in \mathbf{K} \rightarrow \tau \in \mathbf{K}\f$. The dimension \f$n=|\sigma|-1\f$ of
- * \f$\sigma\f$ is its number of elements minus \f$1\f$.
- *
- * A filtration of a simplicial complex is a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying
- * \f$f(\tau)\leq f(\sigma)\f$ whenever \f$\tau \subseteq \sigma\f$. Ordering the simplices by increasing filtration
- * values (breaking ties so as a simplex appears after its subsimplices of same filtration value) provides an
- * indexing scheme.
- *
- * \section filteredcomplexesimplementation Implementations
- * \subsection filteredcomplexessimplextree Simplex tree
- * There are two implementation of complexes. The first on is the Simplex_tree data structure. The simplex tree is an
- * efficient and flexible data structure for representing general (filtered) simplicial complexes. The data structure
- * is described in \cite boissonnatmariasimplextreealgorithmica
- * \image html "Simplex_tree_representation.png" "Simplex tree representation"
- *
- * \subsubsection filteredcomplexessimplextreeexamples Examples
- *
- * Here is a list of simplex tree examples :
- * \li <a href="_simplex_tree_2simple_simplex_tree_8cpp-example.html">
- * Simplex_tree/simple_simplex_tree.cpp</a> - Simple simplex tree construction and basic function use.
- *
- * \li <a href="_simplex_tree_2simplex_tree_from_cliques_of_graph_8cpp-example.html">
- * Simplex_tree/simplex_tree_from_cliques_of_graph.cpp</a> - Simplex tree construction from cliques of graph read in
- * a file.
- *
- * Simplex tree construction with \f$\mathbb{Z}/3\mathbb{Z}\f$ coefficients on weighted graph Klein bottle file:
- * \code $> ./simplex_tree_from_cliques_of_graph ../../data/points/Klein_bottle_complex.txt 3 \endcode
- * \code Insert the 1-skeleton in the simplex tree in 0.000404 s.
-max_dim = 3
-Expand the simplex tree in 3.8e-05 s.
-Information of the Simplex Tree:
-Number of vertices = 10 Number of simplices = 98 \endcode
- *
- * \li <a href="_simplex_tree_2example_alpha_shapes_3_simplex_tree_from_off_file_8cpp-example.html">
- * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp</a> - Simplex tree is computed and displayed
- * from a 3D alpha complex (Requires CGAL, GMP and GMPXX to be installed).
- *
- * \li <a href="_simplex_tree_2graph_expansion_with_blocker_8cpp-example.html">
- * Simplex_tree/graph_expansion_with_blocker.cpp</a> - Simple simplex tree construction from a one-skeleton graph with
- * a simple blocker expansion method.
- *
- * \subsection filteredcomplexeshassecomplex Hasse complex
- * The second one is the Hasse_complex. The Hasse complex is a data structure representing explicitly all co-dimension
- * 1 incidence relations in a complex. It is consequently faster when accessing the boundary of a simplex, but is less
- * compact and harder to construct from scratch.
- *
- * @}
- */
-
-} // namespace Gudhi
-
-#endif // DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_
diff --git a/doc/Simplex_tree/Simplex_tree_representation.png b/doc/Simplex_tree/Simplex_tree_representation.png
deleted file mode 100644
index 9d401520..00000000
--- a/doc/Simplex_tree/Simplex_tree_representation.png
+++ /dev/null
Binary files differ
diff --git a/doc/Skeleton_blocker/COPYRIGHT b/doc/Skeleton_blocker/COPYRIGHT
deleted file mode 100644
index 5b606ac2..00000000
--- a/doc/Skeleton_blocker/COPYRIGHT
+++ /dev/null
@@ -1,18 +0,0 @@
-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): David Salinas
-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/Skeleton_blocker/blocker_curve.svg b/doc/Skeleton_blocker/blocker_curve.svg
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index 0094a379..00000000
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diff --git a/doc/Skeleton_blocker/sphere_contraction.png b/doc/Skeleton_blocker/sphere_contraction.png
deleted file mode 100644
index 502f73f7..00000000
--- a/doc/Skeleton_blocker/sphere_contraction.png
+++ /dev/null
Binary files differ
diff --git a/doc/Spatial_searching/Intro_spatial_searching.h b/doc/Spatial_searching/Intro_spatial_searching.h
deleted file mode 100644
index f387ab2f..00000000
--- a/doc/Spatial_searching/Intro_spatial_searching.h
+++ /dev/null
@@ -1,60 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Clement Jamin
- *
- * Copyright (C) 2016 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/>.
- */
-
-#ifndef DOC_SPATIAL_SEARCHING_INTRO_SPATIAL_SEARCHING_H_
-#define DOC_SPATIAL_SEARCHING_INTRO_SPATIAL_SEARCHING_H_
-
-// needs namespaces for Doxygen to link on classes
-namespace Gudhi {
-namespace spatial_searching {
-
-/** \defgroup spatial_searching Spatial_searching
- *
- * \author Cl&eacute;ment Jamin
- *
- * @{
- *
- * \section introduction Introduction
- *
- * This Gudhi component is a wrapper around
- * <a target="_blank" href="http://doc.cgal.org/latest/Spatial_searching/index.html">CGAL dD spatial searching algorithms</a>.
- * It provides a simplified API to perform (approximate) neighbor searches. Contrary to CGAL default behavior, the tree
- * does not store the points themselves, but stores indices.
- *
- * For more details about the data structure or the algorithms, or for more advanced usages, reading
- * <a target="_blank" href="http://doc.cgal.org/latest/Spatial_searching/index.html">CGAL documentation</a>
- * is highly recommended.
- *
- * \section spatial_searching_examples Example
- *
- * This example generates 500 random points, then performs all-near-neighbors searches, and queries for nearest and furthest neighbors using different methods.
- *
- * \include Spatial_searching/example_spatial_searching.cpp
- *
- */
-/** @} */ // end defgroup spatial_searching
-
-} // namespace spatial_searching
-
-} // namespace Gudhi
-
-#endif // DOC_SPATIAL_SEARCHING_INTRO_SPATIAL_SEARCHING_H_
diff --git a/doc/Subsampling/Intro_subsampling.h b/doc/Subsampling/Intro_subsampling.h
deleted file mode 100644
index d88f6bf6..00000000
--- a/doc/Subsampling/Intro_subsampling.h
+++ /dev/null
@@ -1,68 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Clement Jamin
- *
- * Copyright (C) 2016 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/>.
- */
-
-#ifndef DOC_SUBSAMPLING_INTRO_SUBSAMPLING_H_
-#define DOC_SUBSAMPLING_INTRO_SUBSAMPLING_H_
-
-// needs namespace for Doxygen to link on classes
-namespace Gudhi {
-// needs namespace for Doxygen to link on classes
-namespace subsampling {
-
-/** \defgroup subsampling Subsampling
- *
- * \author Cl&eacute;ment Jamin, Siargey Kachanovich
- *
- * @{
- *
- * \section subsamplingintroduction Introduction
- *
- * This Gudhi component offers methods to subsample a set of points.
- *
- * \section sparsifyexamples Example: sparsify_point_set
- *
- * This example outputs a subset of the input points so that the
- * squared distance between any two points
- * is greater than or equal to 0.4.
- *
- * \include Subsampling/example_sparsify_point_set.cpp
- *
- * \section farthestpointexamples Example: choose_n_farthest_points
- *
- * This example outputs a subset of 100 points obtained by Gonz&aacute;lez algorithm,
- * starting with a random point.
- *
- * \include Subsampling/example_choose_n_farthest_points.cpp
- *
- * \section randompointexamples Example: pick_n_random_points
- *
- * This example outputs a subset of 100 points picked randomly.
- *
- * \include Subsampling/example_pick_n_random_points.cpp
- */
-/** @} */ // end defgroup subsampling
-
-} // namespace subsampling
-
-} // namespace Gudhi
-
-#endif // DOC_SUBSAMPLING_INTRO_SUBSAMPLING_H_
diff --git a/doc/Tangential_complex/COPYRIGHT b/doc/Tangential_complex/COPYRIGHT
deleted file mode 100644
index f9f92471..00000000
--- a/doc/Tangential_complex/COPYRIGHT
+++ /dev/null
@@ -1,19 +0,0 @@
-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): Clement Jamin
-
-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/Tangential_complex/Intro_tangential_complex.h b/doc/Tangential_complex/Intro_tangential_complex.h
deleted file mode 100644
index f4fc8ac7..00000000
--- a/doc/Tangential_complex/Intro_tangential_complex.h
+++ /dev/null
@@ -1,117 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Clement Jamin
- *
- * Copyright (C) 2016 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/>.
- */
-
-#ifndef DOC_TANGENTIAL_COMPLEX_INTRO_TANGENTIAL_COMPLEX_H_
-#define DOC_TANGENTIAL_COMPLEX_INTRO_TANGENTIAL_COMPLEX_H_
-
-// needs namespaces for Doxygen to link on classes
-namespace Gudhi {
-namespace tangential_complex {
-
-/** \defgroup tangential_complex Tangential complex
-
-\author Cl&eacute;ment Jamin
-
-@{
-
-\section tangentialdefinition Definition
-
-A Tangential Delaunay complex is a <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
-designed to reconstruct a \f$k\f$-dimensional smooth manifold embedded in \f$d\f$-dimensional Euclidean space.
-The input is a point sample coming from an unknown manifold, which means that the points lie close to a structure of "small" intrinsic dimension.
-The running time depends only linearly on the extrinsic dimension \f$ d \f$
-and exponentially on the intrinsic dimension \f$ k \f$.
-
-An extensive description of the Tangential complex can be found in \cite tangentialcomplex2014.
-
-\subsection whatisthetc What is a Tangential Complex?
-
-Let us start with the description of the Tangential complex of a simple example, with \f$ k=1 \f$ and \f$ d=2 \f$.
-The input data is 4 points \f$ P \f$ located on a curve embedded in 2D.
-\image html "tc_example_01.png" "The input"
-For each point \f$ p \f$, estimate its tangent subspace \f$ T_p \f$ (e.g. using PCA).
-\image html "tc_example_02.png" "The estimated normals"
-Let us add the Voronoi diagram of the points in orange. For each point \f$ p \f$, construct its star in the Delaunay triangulation of \f$ P \f$ restricted to \f$ T_p \f$.
-\image html "tc_example_03.png" "The Voronoi diagram"
-The Tangential Delaunay complex is the union of those stars.
-
-In practice, neither the ambient Voronoi diagram nor the ambient Delaunay triangulation is computed.
-Instead, local \f$ k \f$-dimensional regular triangulations are computed with a limited number of points as we only need the star of each point.
-More details can be found in \cite tangentialcomplex2014.
-
-\subsection inconsistencies Inconsistencies
-
-Inconsistencies between the stars can occur.
-An inconsistency occurs when a simplex is not in the star of all its vertices.
-
-Let us take the same example.
-\image html "tc_example_07_before.png" "Before"
-Let us slightly move the tangent subspace \f$ T_q \f$
-\image html "tc_example_07_after.png" "After"
-Now, the star of \f$ Q \f$ contains \f$ QP \f$, but the star of \f$ P \f$ does not contain \f$ QP \f$. We have an inconsistency.
-\image html "tc_example_08.png" "After"
-
-One way to solve inconsistencies is to randomly perturb the positions of the points involved in an inconsistency.
-In the current implementation, this perturbation is done in the tangent subspace of each point.
-The maximum perturbation radius is given as a parameter to the constructor.
-
-In most cases, we recommend to provide a point set where the minimum distance between any two points
-is not too small. This can be achieved using the functions provided by the Subsampling module. Then, a good value to start with for
-the maximum perturbation radius would be around half the minimum distance between any two points.
-The \ref example_with_perturb below shows an example of such a process.
-
-In most cases, this process is able to dramatically reduce the number of inconsistencies, but is not guaranteed to succeed.
-
-\subsection output Output
-
-The result of the computation is exported as a `Simplex_tree`. It is the union of the stars of all the input points.
-A vertex in the Simplex Tree is the index of the point in the range provided by the user.
-The point corresponding to a vertex can also be obtained through the `Tangential_complex::get_point` function.
-Note that even if the positions of the points are perturbed, their original positions are kept (e.g. `Tangential_complex::get_point` returns the original position of the point).
-
-The result can be obtained after the computation of the Tangential complex itself and/or after the perturbation process.
-
-\section simple_example Simple example
-
-This example builds the Tangential complex of point set.
-Note that the dimension of the kernel here is dynamic, which is slower, but more flexible:
-the intrinsic and ambient dimensions does not have to be known at compile-time.
-
-\include Tangential_complex/example_basic.cpp
-
-\section example_with_perturb Example with perturbation
-
-This example builds the Tangential complex of a point set, then tries to solve inconsistencies
-by perturbing the positions of points involved in inconsistent simplices.
-Note that the dimension of the kernel here is static, which is the best choice when the
-dimensions are known at compile-time.
-
-\include Tangential_complex/example_with_perturb.cpp
-
- */
-/** @} */ // end defgroup tangential_complex
-
-} // namespace tangential_complex
-
-} // namespace Gudhi
-
-#endif // DOC_TANGENTIAL_COMPLEX_INTRO_TANGENTIAL_COMPLEX_H_
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diff --git a/doc/Witness_complex/COPYRIGHT b/doc/Witness_complex/COPYRIGHT
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index 25a700cf..00000000
--- a/doc/Witness_complex/COPYRIGHT
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@@ -1,19 +0,0 @@
-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
--- a/doc/Witness_complex/Witness_complex_doc.h
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@@ -1,122 +0,0 @@
-#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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- </g>
-</svg>
diff --git a/doc/common/Gudhi_banner.png b/doc/common/Gudhi_banner.png
deleted file mode 100644
index 18e8a672..00000000
--- a/doc/common/Gudhi_banner.png
+++ /dev/null
Binary files differ
diff --git a/doc/common/examples.h b/doc/common/examples.h
deleted file mode 100644
index 40f202c7..00000000
--- a/doc/common/examples.h
+++ /dev/null
@@ -1,99 +0,0 @@
-// List of GUDHI examples - Doxygen needs at least a file tag to analyse comments
-// In user_version, `find . -name "*.cpp"` in example and utilities folders
-/*! @file Examples
- * @example Alpha_complex/Alpha_complex_from_off.cpp
- * @example Alpha_complex/Alpha_complex_from_points.cpp
- * @example Bottleneck_distance/bottleneck_basic_example.cpp
- * @example Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp
- * @example Witness_complex/example_nearest_landmark_table.cpp
- * @example Witness_complex/example_witness_complex_off.cpp
- * @example Witness_complex/example_witness_complex_sphere.cpp
- * @example Witness_complex/example_strong_witness_complex_off.cpp
- * @example Simplex_tree/mini_simplex_tree.cpp
- * @example Simplex_tree/graph_expansion_with_blocker.cpp
- * @example Simplex_tree/simple_simplex_tree.cpp
- * @example Simplex_tree/simplex_tree_from_cliques_of_graph.cpp
- * @example Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp
- * @example Simplex_tree/cech_complex_cgal_mini_sphere_3d.cpp
- * @example Persistent_cohomology/plain_homology.cpp
- * @example Persistent_cohomology/persistence_from_file.cpp
- * @example Persistent_cohomology/rips_persistence_step_by_step.cpp
- * @example Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp
- * @example Persistent_cohomology/custom_persistence_sort.cpp
- * @example Persistent_cohomology/persistence_from_simple_simplex_tree.cpp
- * @example Persistent_cohomology/rips_multifield_persistence.cpp
- * @example Skeleton_blocker/Skeleton_blocker_from_simplices.cpp
- * @example Skeleton_blocker/Skeleton_blocker_iteration.cpp
- * @example Skeleton_blocker/Skeleton_blocker_link.cpp
- * @example Contraction/Garland_heckbert.cpp
- * @example Contraction/Rips_contraction.cpp
- * @example Bitmap_cubical_complex/Random_bitmap_cubical_complex.cpp
- * @example common/example_CGAL_3D_points_off_reader.cpp
- * @example common/example_vector_double_points_off_reader.cpp
- * @example common/example_CGAL_points_off_reader.cpp
- * @example Rips_complex/example_one_skeleton_rips_from_distance_matrix.cpp
- * @example Rips_complex/example_one_skeleton_rips_from_points.cpp
- * @example Rips_complex/example_rips_complex_from_csv_distance_matrix_file.cpp
- * @example Rips_complex/example_rips_complex_from_off_file.cpp
- * @example Persistence_representations/persistence_intervals.cpp
- * @example Persistence_representations/persistence_vectors.cpp
- * @example Persistence_representations/persistence_heat_maps.cpp
- * @example Persistence_representations/persistence_landscape_on_grid.cpp
- * @example Persistence_representations/persistence_landscape.cpp
- * @example Tangential_complex/example_basic.cpp
- * @example Tangential_complex/example_with_perturb.cpp
- * @example Subsampling/example_custom_kernel.cpp
- * @example Subsampling/example_choose_n_farthest_points.cpp
- * @example Subsampling/example_sparsify_point_set.cpp
- * @example Subsampling/example_pick_n_random_points.cpp
- * @example Nerve_GIC/CoordGIC.cpp
- * @example Nerve_GIC/Nerve.cpp
- * @example Nerve_GIC/FuncGIC.cpp
- * @example Nerve_GIC/VoronoiGIC.cpp
- * @example Spatial_searching/example_spatial_searching.cpp
- * @example Alpha_complex/alpha_complex_3d_persistence.cpp
- * @example Alpha_complex/alpha_complex_persistence.cpp
- * @example Alpha_complex/weighted_periodic_alpha_complex_3d_persistence.cpp
- * @example Alpha_complex/weighted_alpha_complex_3d_persistence.cpp
- * @example Alpha_complex/periodic_alpha_complex_3d_persistence.cpp
- * @example Alpha_complex/exact_alpha_complex_3d_persistence.cpp
- * @example Bottleneck_distance/bottleneck_distance.cpp
- * @example Witness_complex/weak_witness_persistence.cpp
- * @example Witness_complex/strong_witness_persistence.cpp
- * @example Bitmap_cubical_complex/cubical_complex_persistence.cpp
- * @example Bitmap_cubical_complex/periodic_cubical_complex_persistence.cpp
- * @example common/off_file_from_shape_generator.cpp
- * @example Rips_complex/rips_distance_matrix_persistence.cpp
- * @example Rips_complex/rips_persistence.cpp
- * @example Persistence_representations/persistence_landscapes_on_grid/create_landscapes_on_grid.cpp
- * @example Persistence_representations/persistence_landscapes_on_grid/plot_landscapes_on_grid.cpp
- * @example Persistence_representations/persistence_landscapes_on_grid/compute_scalar_product_of_landscapes_on_grid.cpp
- * @example Persistence_representations/persistence_landscapes_on_grid/compute_distance_of_landscapes_on_grid.cpp
- * @example Persistence_representations/persistence_landscapes_on_grid/average_landscapes_on_grid.cpp
- * @example Persistence_representations/persistence_intervals/compute_birth_death_range_in_persistence_diagram.cpp
- * @example Persistence_representations/persistence_intervals/compute_number_of_dominant_intervals.cpp
- * @example Persistence_representations/persistence_intervals/plot_persistence_Betti_numbers.cpp
- * @example Persistence_representations/persistence_intervals/plot_persistence_intervals.cpp
- * @example Persistence_representations/persistence_intervals/plot_histogram_of_intervals_lengths.cpp
- * @example Persistence_representations/persistence_intervals/compute_bottleneck_distance.cpp
- * @example Persistence_representations/persistence_heat_maps/create_pssk.cpp
- * @example Persistence_representations/persistence_heat_maps/create_p_h_m_weighted_by_arctan_of_their_persistence.cpp
- * @example Persistence_representations/persistence_heat_maps/create_p_h_m_weighted_by_squared_diag_distance.cpp
- * @example Persistence_representations/persistence_heat_maps/compute_distance_of_persistence_heat_maps.cpp
- * @example Persistence_representations/persistence_heat_maps/compute_scalar_product_of_persistence_heat_maps.cpp
- * @example Persistence_representations/persistence_heat_maps/create_p_h_m_weighted_by_distance_from_diagonal.cpp
- * @example Persistence_representations/persistence_heat_maps/average_persistence_heat_maps.cpp
- * @example Persistence_representations/persistence_heat_maps/plot_persistence_heat_map.cpp
- * @example Persistence_representations/persistence_heat_maps/create_persistence_heat_maps.cpp
- * @example Persistence_representations/persistence_vectors/plot_persistence_vectors.cpp
- * @example Persistence_representations/persistence_vectors/compute_distance_of_persistence_vectors.cpp
- * @example Persistence_representations/persistence_vectors/average_persistence_vectors.cpp
- * @example Persistence_representations/persistence_vectors/create_persistence_vectors.cpp
- * @example Persistence_representations/persistence_vectors/compute_scalar_product_of_persistence_vectors.cpp
- * @example Persistence_representations/persistence_landscapes/average_landscapes.cpp
- * @example Persistence_representations/persistence_landscapes/compute_scalar_product_of_landscapes.cpp
- * @example Persistence_representations/persistence_landscapes/create_landscapes.cpp
- * @example Persistence_representations/persistence_landscapes/compute_distance_of_landscapes.cpp
- * @example Persistence_representations/persistence_landscapes/plot_landscapes.cpp
- */
-
diff --git a/doc/common/file_formats.h b/doc/common/file_formats.h
deleted file mode 100644
index 523153b8..00000000
--- a/doc/common/file_formats.h
+++ /dev/null
@@ -1,125 +0,0 @@
-/* This file is part of the Gudhi Library. The Gudhi library
-* (Geometric Understanding in Higher Dimensions) is a generic C++
-* library for computational topology.
-*
-* Author(s): Clément Jamin
-*
-* Copyright (C) 2017 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/>.
-*/
-
-#ifndef DOC_COMMON_FILE_FORMAT_H_
-#define DOC_COMMON_FILE_FORMAT_H_
-
-namespace Gudhi {
-
-/*! \page fileformats File formats
-
- \tableofcontents
-
- \section FileFormatsPers Persistence Diagram
-
- Such a file, whose extension is usually `.pers`, contains a list of persistence intervals.<br>
- Lines starting with `#` are ignored (comments).<br>
- Other lines might contain 2, 3 or 4 values (the number of values on each line must be the same for all lines):
- \verbatim
- [[field] dimension] birth death
- \endverbatim
-
- Here is a simple sample file:
- \verbatim
- # Persistence diagram example
- 2 2.7 3.7
- 2 9.6 14.
- # Some comments
- 3 34.2 34.974
- 4 3. inf
- \endverbatim
-
- Other sample files can be found in the `data/persistence_diagram` folder.
-
- Such files can be generated with `Gudhi::persistent_cohomology::Persistent_cohomology::output_diagram()` and read with
- `Gudhi::read_persistence_intervals_and_dimension()`, `Gudhi::read_persistence_intervals_grouped_by_dimension()` or
- `Gudhi::read_persistence_intervals_in_dimension()`.
-
-
- \section FileFormatsIsoCuboid Iso-cuboid
-
- Such a file describes an iso-oriented cuboid with diagonal opposite vertices (min_x, min_y, min_z,...) and (max_x, max_y, max_z, ...). The format is:<br>
- \verbatim
- min_x min_y [min_z ...]
- max_x max_y [max_z ...]
- \endverbatim
-
- Here is a simple sample file in the 3D case:
- \verbatim
- -1. -1. -1.
- 1. 1. 1.
- \endverbatim
-
-
- \section FileFormatsPerseus Perseus
-
- This file format is the format used by the Perseus software
- (http://www.sas.upenn.edu/~vnanda/perseus/) by Vidit Nanda.
- The first line contains a number d begin the dimension of the
- bitmap (2 in the example below). Next d lines are the numbers of top dimensional cubes in each dimensions (3 and 3
- in the example below). Next, in lexicographical order, the filtration of top dimensional cubes is given (1 4 6 8
- 20 4 7 6 5 in the example below).
-
- \image html "exampleBitmap.png" "Example of a input data."
-
- The input file for the following complex is:
- \verbatim
- 2
- 3
- 3
- 1
- 4
- 6
- 8
- 20
- 4
- 7
- 6
- 5
- \endverbatim
-
- To indicate periodic boundary conditions in a
- given direction, then number of top dimensional cells in this direction have to be multiplied by -1. For instance:
-
- \verbatim
- 2
- -3
- 3
- 1
- 4
- 6
- 8
- 20
- 4
- 7
- 6
- 5
- \endverbatim
-
- Indicate that we have imposed periodic boundary conditions in the direction x, but not in the direction y.
-
- Other sample files can be found in the `data/bitmap` folder.
-
-*/
-} // namespace Gudhi
-
-#endif // DOC_COMMON_FILE_FORMAT_H_
diff --git a/doc/common/footer.html b/doc/common/footer.html
deleted file mode 100644
index a557922b..00000000
--- a/doc/common/footer.html
+++ /dev/null
@@ -1,23 +0,0 @@
-<!-- HTML footer for doxygen 1.8.6-->
-<!-- start footer part -->
-<table style="width:100%">
- <tr class="no-bullet shadow-black">
- <td class="network-entypo">
-<!--BEGIN PROJECT_NAME--> $projectname
-<!--BEGIN PROJECT_NUMBER-->&#160;Version $projectnumber<!--END PROJECT_NUMBER-->
-<!--BEGIN PROJECT_BRIEF-->&#160;-&#160;$projectbrief<!--END PROJECT_BRIEF-->
-<!--BEGIN PROJECT_BRIEF-->&#160;-&#160;Copyright : GPL v3<!--END PROJECT_BRIEF-->
-<!--END PROJECT_NAME-->
- </td>
- <td class="network-entypo">
-<!--BEGIN GENERATE_TREEVIEW-->
- $generatedby
- <a href="http://www.doxygen.org/index.html">
- Doxygen</a> $doxygenversion
-<!--END GENERATE_TREEVIEW-->
- </td>
- </tr>
-</table>
-
-</body>
-</html>
diff --git a/doc/common/header.html b/doc/common/header.html
deleted file mode 100644
index c12d2816..00000000
--- a/doc/common/header.html
+++ /dev/null
@@ -1,102 +0,0 @@
-<!-- HTML header for doxygen 1.8.6-->
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<!-- GUDHI website : class="no-js" lang="en" is necessary -->
-<html xmlns="http://www.w3.org/1999/xhtml" class="no-js" lang="en">
-<head>
-<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
-<meta http-equiv="X-UA-Compatible" content="IE=9"/>
-<meta name="generator" content="Doxygen $doxygenversion"/>
-<!--BEGIN PROJECT_NAME--><title>$projectname: $title</title><!--END PROJECT_NAME-->
-<!--BEGIN !PROJECT_NAME--><title>$title</title><!--END !PROJECT_NAME-->
-<!-- GUDHI website css for header BEGIN -->
-<link rel="stylesheet" type="text/css" href="https://gudhi.inria.fr/assets/css/styles_feeling_responsive.css" />
-<!-- GUDHI website css for header END -->
-<link href="$relpath^tabs.css" rel="stylesheet" type="text/css"/>
-<script type="text/javascript" src="$relpath^jquery.js"></script>
-<script type="text/javascript" src="$relpath^dynsections.js"></script>
-$treeview
-$search
-$mathjax
-<link href="$relpath^$stylesheet" rel="stylesheet" type="text/css" />
-$extrastylesheet
-</head>
-<body>
-
-<!-- GUDHI website header BEGIN -->
-<div id="navigation" class="sticky">
- <nav class="top-bar" role="navigation" data-topbar>
- <ul class="title-area">
- <li class="name">
- <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI C++ library</a></h1>
- </li>
- <!-- Remove the class "menu-icon" to get rid of menu icon. Take out "Menu" to just have icon alone -->
- <li class="toggle-topbar menu-icon"><a href="#"><span>Navigation</span></a></li>
- </ul>
- <section class="top-bar-section">
- <ul class="right">
- <li class="divider"></li>
- <li><a href="/contact/">Contact</a></li>
- </ul>
- <ul class="left">
- <li><a href="/"> <img src="/assets/img/home.png" alt="&nbsp;&nbsp;GUDHI">&nbsp;&nbsp;GUDHI </a></li>
- <li class="divider"></li>
- <li class="has-dropdown">
- <a href="#">Project</a>
- <ul class="dropdown">
- <li><a href="/people/">People</a></li>
- <li><a href="/keepintouch/">Keep in touch</a></li>
- <li><a href="/partners/">Partners and Funding</a></li>
- <li><a href="/relatedprojects/">Related projects</a></li>
- <li><a href="/theyaretalkingaboutus/">They are talking about us</a></li>
- </ul>
- </li>
- <li class="divider"></li>
- <li class="has-dropdown">
- <a href="#">Download</a>
- <ul class="dropdown">
- <li><a href="/licensing/">Licensing</a></li>
- <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5253/library-latest.zip" target="_blank">Get the latest sources</a></li>
- <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5280/utils_osx-latest.zip" target="_blank">Utils for Mac OSx</a></li>
- <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5279/utils_win64-latest.zip" target="_blank">Utils for Win x64</a></li>
- </ul>
- </li>
- <li class="divider"></li>
- <li class="has-dropdown">
- <a href="#">Documentation</a>
- <ul class="dropdown">
- <li><a href="/doc/latest/">C++ documentation</a></li>
- <li><a href="/doc/latest/installation.html">C++ installation manual</a></li>
- <li><a href="/python/latest/">Python documentation</a></li>
- <li><a href="/python/latest/installation.html">Python installation manual</a></li>
- <li><a href="/utils/">Utilities</a></li>
- <li><a href="/tutorials/">Tutorials</a></li>
- <li><a href="/dockerfile/">Dockerfile</a></li>
- </ul>
- </li>
- <li class="divider"></li>
- <li><a href="/interfaces/">Interfaces</a></li>
- <li class="divider"></li>
- </ul>
- </section>
- </nav>
-</div><!-- /#navigation -->
-<!-- GUDHI website header BEGIN -->
-
-<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
-
-<!--BEGIN TITLEAREA-->
-<div id="titlearea">
-<table cellspacing="0" cellpadding="0">
- <tbody>
- <tr style="height: 30px;">
- <!--BEGIN DISABLE_INDEX-->
- <!--BEGIN SEARCHENGINE-->
- <td>$searchbox</td>
- <!--END SEARCHENGINE-->
- <!--END DISABLE_INDEX-->
- </tr>
- </tbody>
-</table>
-</div>
-<!--END TITLEAREA-->
-<!-- end header part -->
diff --git a/doc/common/installation.h b/doc/common/installation.h
deleted file mode 100644
index c27e4f56..00000000
--- a/doc/common/installation.h
+++ /dev/null
@@ -1,280 +0,0 @@
-/*! \page installation GUDHI installation
- * \tableofcontents
- * As GUDHI is a header only library, there is no need to install the library.
- *
- * Examples of GUDHI headers inclusion can be found in \ref utilities.
- *
- * \section compiling Compiling
- * The library uses c++11 and requires <a target="_blank" href="http://www.boost.org/">Boost</a> &ge; 1.48.0
- * and <a target="_blank" href="https://www.cmake.org/">CMake</a> &ge; 3.1.
- * It is a multi-platform library and compiles on Linux, Mac OSX and Visual Studio 2015.
- *
- * \subsection utilities Utilities and examples
- * To build the utilities, run the following commands in a terminal:
-\verbatim cd /path-to-gudhi/
-mkdir build
-cd build/
-cmake ..
-make \endverbatim
- * By default, examples are disabled. You can activate their compilation with
- * <a href="https://cmake.org/cmake/help/v3.0/manual/ccmake.1.html">ccmake</a> (on Linux and Mac OSX),
- * <a href="https://cmake.org/cmake/help/v3.0/manual/cmake-gui.1.html">cmake-gui</a> (on Windows) or y mofifying the
- * cmake command as follows :
-\verbatim cmake -DWITH_GUDHI_EXAMPLE=ON ..
-make \endverbatim
- * A list of utilities and examples is available <a href="examples.html">here</a>.
- *
- * \subsection libraryinstallation Installation
- * To install the library (headers and activated utilities), run the following command in a terminal:
- * \verbatim make install \endverbatim
- * This action may require to be in the sudoer or administrator of the machine in function of the operating system and
- * of <a href="https://cmake.org/cmake/help/v3.0/variable/CMAKE_INSTALL_PREFIX.html">CMAKE_INSTALL_PREFIX</a>.
- *
- * \subsection testsuites Test suites
- * To test your build, run the following command in a terminal:
- * \verbatim make test \endverbatim
- *
- * \subsection documentationgeneration Documentation
- * To generate the documentation, <a target="_blank" href="http://www.doxygen.org/">Doxygen</a> is required.
- * Run the following command in a terminal:
-\verbatim
-make doxygen
-# Documentation will be generated in the folder YYYY-MM-DD-hh-mm-ss_GUDHI_X.Y.Z/doc/html/
-# You can customize the directory name by calling `cmake -DUSER_VERSION_DIR=/my/custom/folder`
-\endverbatim
- *
- * \subsection helloworld Hello world !
- * The <a target="_blank" href="https://gitlab.inria.fr/GUDHI/hello-gudhi-world">Hello world for GUDHI</a>
- * project is an example to help developers to make their own C++ project on top of the GUDHI library.
- *
- * \section optionallibrary Optional third-party library
- * \subsection gmp GMP
- * The multi-field persistent homology algorithm requires GMP which is a free library for arbitrary-precision
- * arithmetic, operating on signed integers, rational numbers, and floating point numbers.
- *
- * The following example requires the <a target="_blank" href="http://gmplib.org/">GNU Multiple Precision Arithmetic
- * Library</a> (GMP) and will not be built if GMP is not installed:
- * \li <a href="_persistent_cohomology_2rips_multifield_persistence_8cpp-example.html">
- * Persistent_cohomology/rips_multifield_persistence.cpp</a>
- *
- * Having GMP version 4.2 or higher installed is recommended.
- *
- * \subsection cgal CGAL
- * The \ref alpha_complex data structure, \ref bottleneck_distance, and few examples requires CGAL, which is a C++
- * library which provides easy access to efficient and reliable geometric algorithms.
- *
- * \note There is no need to install CGAL, you can just <CODE>cmake . && make</CODE> CGAL (or even
- * <CODE>cmake -DCGAL_HEADER_ONLY=ON .</CODE> for CGAL version &ge; 4.8.0), thereafter you will be able to compile
- * GUDHI by calling <CODE>cmake -DCGAL_DIR=/your/path/to/CGAL-X.Y .. && make</CODE>
- *
- * Having CGAL version 4.4.0 or higher installed is recommended. The procedure to install this library according to
- * your operating system is detailed here http://doc.cgal.org/latest/Manual/installation.html
- *
- * The following examples/utilities require the <a target="_blank" href="http://www.cgal.org/">Computational Geometry Algorithms
- * Library</a> (CGAL \cite cgal:eb-15b) and will not be built if CGAL is not installed:
- * \li <a href="_alpha_complex_2alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2exact_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/exact_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/weighted_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_simplex_tree_2example_alpha_shapes_3_simplex_tree_from_off_file_8cpp-example.html">
- * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp</a>
- *
- * The following examples/utilities require CGAL version &ge; 4.6.0:
- * \li <a href="_witness_complex_2strong_witness_persistence_8cpp-example.html">
- * Witness_complex/strong_witness_persistence.cpp</a>
- * \li <a href="_witness_complex_2weak_witness_persistence_8cpp-example.html">
- * Witness_complex/weak_witness_persistence.cpp</a>
- * \li <a href="_witness_complex_2example_strong_witness_complex_off_8cpp-example.html">
- * Witness_complex/example_strong_witness_complex_off.cpp</a>
- * \li <a href="_witness_complex_2example_witness_complex_off_8cpp-example.html">
- * Witness_complex/example_witness_complex_off.cpp</a>
- * \li <a href="_witness_complex_2example_witness_complex_sphere_8cpp-example.html">
- * Witness_complex/example_witness_complex_sphere.cpp</a>
- *
- * The following example requires CGAL version &ge; 4.7.0:
- * \li <a href="_alpha_complex_2_alpha_complex_from_off_8cpp-example.html">
- * Alpha_complex/Alpha_complex_from_off.cpp</a>
- * \li <a href="_alpha_complex_2_alpha_complex_from_points_8cpp-example.html">
- * Alpha_complex/Alpha_complex_from_points.cpp</a>
- * \li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html">
- * Alpha_complex/alpha_complex_persistence.cpp</a>
- * \li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_persistent_cohomology_2custom_persistence_sort_8cpp-example.html">
- * Persistent_cohomology/custom_persistence_sort.cpp</a>
- *
- * The following example requires CGAL version &ge; 4.8.1:
- * \li <a href="_bottleneck_distance_2alpha_rips_persistence_bottleneck_distance_8cpp-example.html">
- * Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp.cpp</a>
- * \li <a href="_bottleneck_distance_2bottleneck_basic_example_8cpp-example.html">
- * Bottleneck_distance/bottleneck_basic_example.cpp</a>
- * \li <a href="_bottleneck_distance_2bottleneck_read_file_8cpp-example.html">
- * Bottleneck_distance/bottleneck_distance.cpp</a>
- * \li <a href="_nerve__g_i_c_2_coord_g_i_c_8cpp-example.html">
- * Nerve_GIC/CoordGIC.cpp</a>
- * \li <a href="_nerve__g_i_c_2_func_g_i_c_8cpp-example.html">
- * Nerve_GIC/FuncGIC.cpp</a>
- * \li <a href="_nerve__g_i_c_2_nerve_8cpp-example.html">
- * Nerve_GIC/Nerve.cpp</a>
- * \li <a href="_nerve__g_i_c_2_voronoi_g_i_c_8cpp-example.html">
- * Nerve_GIC/VoronoiGIC.cpp</a>
- * \li <a href="_spatial_searching_2example_spatial_searching_8cpp-example.html">
- * Spatial_searching/example_spatial_searching.cpp</a>
- * \li <a href="_subsampling_2example_choose_n_farthest_points_8cpp-example.html">
- * Subsampling/example_choose_n_farthest_points.cpp</a>
- * \li <a href="_subsampling_2example_custom_kernel_8cpp-example.html">
- * Subsampling/example_custom_kernel.cpp</a>
- * \li <a href="_subsampling_2example_pick_n_random_points_8cpp-example.html">
- * Subsampling/example_pick_n_random_points.cpp</a>
- * \li <a href="_subsampling_2example_sparsify_point_set_8cpp-example.html">
- * Subsampling/example_sparsify_point_set.cpp</a>
- * \li <a href="_tangential_complex_2example_basic_8cpp-example.html">
- * Tangential_complex/example_basic.cpp</a>
- * \li <a href="_tangential_complex_2example_with_perturb_8cpp-example.html">
- * Tangential_complex/example_with_perturb.cpp</a>
- *
- * \subsection eigen3 Eigen3
- * The \ref alpha_complex data structure and few examples requires
- * <a target="_blank" href="http://eigen.tuxfamily.org/">Eigen3</a> is a C++ template library for linear algebra:
- * matrices, vectors, numerical solvers, and related algorithms.
- *
- * The following examples/utilities require the <a target="_blank" href="http://eigen.tuxfamily.org/">Eigen3</a> and will not be
- * built if Eigen3 is not installed:
- * \li <a href="_alpha_complex_2_alpha_complex_from_off_8cpp-example.html">
- * Alpha_complex/Alpha_complex_from_off.cpp</a>
- * \li <a href="_alpha_complex_2_alpha_complex_from_points_8cpp-example.html">
- * Alpha_complex/Alpha_complex_from_points.cpp</a>
- * \li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html">
- * Alpha_complex/alpha_complex_persistence.cpp</a>
- * \li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_bottleneck_distance_2alpha_rips_persistence_bottleneck_distance_8cpp-example.html">
- * Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp.cpp</a>
- * \li <a href="_persistent_cohomology_2custom_persistence_sort_8cpp-example.html">
- * Persistent_cohomology/custom_persistence_sort.cpp</a>
- * \li <a href="_spatial_searching_2example_spatial_searching_8cpp-example.html">
- * Spatial_searching/example_spatial_searching.cpp</a>
- * \li <a href="_subsampling_2example_choose_n_farthest_points_8cpp-example.html">
- * Subsampling/example_choose_n_farthest_points.cpp</a>
- * \li <a href="_subsampling_2example_custom_kernel_8cpp-example.html">
- * Subsampling/example_custom_kernel.cpp</a>
- * \li <a href="_subsampling_2example_pick_n_random_points_8cpp-example.html">
- * Subsampling/example_pick_n_random_points.cpp</a>
- * \li <a href="_subsampling_2example_sparsify_point_set_8cpp-example.html">
- * Subsampling/example_sparsify_point_set.cpp</a>
- * \li <a href="_tangential_complex_2example_basic_8cpp-example.html">
- * Tangential_complex/example_basic.cpp</a>
- * \li <a href="_tangential_complex_2example_with_perturb_8cpp-example.html">
- * Tangential_complex/example_with_perturb.cpp</a>
- * \li <a href="_witness_complex_2strong_witness_persistence_8cpp-example.html">
- * Witness_complex/strong_witness_persistence.cpp</a>
- * \li <a href="_witness_complex_2weak_witness_persistence_8cpp-example.html">
- * Witness_complex/weak_witness_persistence.cpp</a>
- * \li <a href="_witness_complex_2example_strong_witness_complex_off_8cpp-example.html">
- * Witness_complex/example_strong_witness_complex_off.cpp</a>
- * \li <a href="_witness_complex_2example_witness_complex_off_8cpp-example.html">
- * Witness_complex/example_witness_complex_off.cpp</a>
- * \li <a href="_witness_complex_2example_witness_complex_sphere_8cpp-example.html">
- * Witness_complex/example_witness_complex_sphere.cpp</a>
- *
- * \subsection tbb Threading Building Blocks
- * <a target="_blank" href="https://www.threadingbuildingblocks.org/">Intel&reg; TBB</a> lets you easily write parallel
- * C++ programs that take full advantage of multicore performance, that are portable and composable, and that have
- * future-proof scalability.
- *
- * Having Intel&reg; TBB installed is recommended to parallelize and accelerate some GUDHI computations.
- *
- * The following examples/utilities are using Intel&reg; TBB if installed:
- * \li <a href="_alpha_complex_2_alpha_complex_from_off_8cpp-example.html">
- * Alpha_complex/Alpha_complex_from_off.cpp</a>
- * \li <a href="_alpha_complex_2_alpha_complex_from_points_8cpp-example.html">
- * Alpha_complex/Alpha_complex_from_points.cpp</a>
- * \li <a href="_alpha_complex_2alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html">
- * Alpha_complex/alpha_complex_persistence.cpp</a>
- * \li <a href="_alpha_complex_2exact_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/exact_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_alpha_complex_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
- * Alpha_complex/weighted_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_bitmap_cubical_complex_2_bitmap_cubical_complex_8cpp-example.html">
- * Bitmap_cubical_complex/cubical_complex_persistence.cpp</a>
- * \li <a href="_bitmap_cubical_complex_2_bitmap_cubical_complex_periodic_boundary_conditions_8cpp-example.html">
- * Bitmap_cubical_complex/periodic_cubical_complex_persistence.cpp</a>
- * \li <a href="_bitmap_cubical_complex_2_random_bitmap_cubical_complex_8cpp-example.html">
- * Bitmap_cubical_complex/Random_bitmap_cubical_complex.cpp</a>
- * \li <a href="_nerve__g_i_c_2_coord_g_i_c_8cpp-example.html">
- * Nerve_GIC/CoordGIC.cpp</a>
- * \li <a href="_nerve__g_i_c_2_func_g_i_c_8cpp-example.html">
- * Nerve_GIC/FuncGIC.cpp</a>
- * \li <a href="_nerve__g_i_c_2_nerve_8cpp-example.html">
- * Nerve_GIC/Nerve.cpp</a>
- * \li <a href="_nerve__g_i_c_2_voronoi_g_i_c_8cpp-example.html">
- * Nerve_GIC/VoronoiGIC.cpp</a>
- * \li <a href="_simplex_tree_2simple_simplex_tree_8cpp-example.html">
- * Simplex_tree/simple_simplex_tree.cpp</a>
- * \li <a href="_simplex_tree_2example_alpha_shapes_3_simplex_tree_from_off_file_8cpp-example.html">
- * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp</a>
- * \li <a href="_simplex_tree_2simplex_tree_from_cliques_of_graph_8cpp-example.html">
- * Simplex_tree/simplex_tree_from_cliques_of_graph.cpp</a>
- * \li <a href="_simplex_tree_2graph_expansion_with_blocker_8cpp-example.html">
- * Simplex_tree/graph_expansion_with_blocker.cpp</a>
- * \li <a href="_persistent_cohomology_2alpha_complex_3d_persistence_8cpp-example.html">
- * Persistent_cohomology/alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_persistent_cohomology_2alpha_complex_persistence_8cpp-example.html">
- * Persistent_cohomology/alpha_complex_persistence.cpp</a>
- * \li <a href="_persistent_cohomology_2rips_persistence_via_boundary_matrix_8cpp-example.html">
- * Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp</a>
- * \li <a href="_persistent_cohomology_2persistence_from_file_8cpp-example.html">
- * Persistent_cohomology/persistence_from_file.cpp</a>
- * \li <a href="_persistent_cohomology_2persistence_from_simple_simplex_tree_8cpp-example.html">
- * Persistent_cohomology/persistence_from_simple_simplex_tree.cpp</a>
- * \li <a href="_persistent_cohomology_2plain_homology_8cpp-example.html">
- * Persistent_cohomology/plain_homology.cpp</a>
- * \li <a href="_persistent_cohomology_2rips_multifield_persistence_8cpp-example.html">
- * Persistent_cohomology/rips_multifield_persistence.cpp</a>
- * \li <a href="_persistent_cohomology_2rips_persistence_step_by_step_8cpp-example.html">
- * Persistent_cohomology/rips_persistence_step_by_step.cpp</a>
- * \li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html">
- * Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_persistent_cohomology_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
- * Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp</a>
- * \li <a href="_persistent_cohomology_2custom_persistence_sort_8cpp-example.html">
- * Persistent_cohomology/custom_persistence_sort.cpp</a>
- * \li <a href="_rips_complex_2example_one_skeleton_rips_from_points_8cpp-example.html">
- * Rips_complex/example_one_skeleton_rips_from_points.cpp</a>
- * \li <a href="_rips_complex_2example_rips_complex_from_off_file_8cpp-example.html">
- * Rips_complex/example_rips_complex_from_off_file.cpp</a>
- * \li <a href="_rips_complex_2rips_distance_matrix_persistence_8cpp-example.html">
- * Rips_complex/rips_distance_matrix_persistence.cpp</a>
- * \li <a href="_rips_complex_2rips_persistence_8cpp-example.html">
- * Rips_complex/rips_persistence.cpp</a>
- * \li <a href="_witness_complex_2strong_witness_persistence_8cpp-example.html">
- * Witness_complex/strong_witness_persistence.cpp</a>
- * \li <a href="_witness_complex_2weak_witness_persistence_8cpp-example.html">
- * Witness_complex/weak_witness_persistence.cpp</a>
- * \li <a href="_witness_complex_2example_nearest_landmark_table_8cpp-example.html">
- * Witness_complex/example_nearest_landmark_table.cpp</a>
- *
- * \section Contributions Bug reports and contributions
- * Please help us improving the quality of the GUDHI library. You may report bugs or suggestions to:
- * \verbatim Contact: gudhi-users@lists.gforge.inria.fr \endverbatim
- *
- * GUDHI is open to external contributions. If you want to join our development team, please contact us.
- *
-*/
-
-/*! \page Citation Acknowledging the GUDHI library
- * We kindly ask users to cite the GUDHI library as appropriately as possible in their papers, and to mention the use
- * of the GUDHI library on the web pages of their projects using GUDHI and provide us with links to these web pages.
- * Feel free to contact us in case you have any question or remark on this topic.
- *
- * We provide \ref GudhiBibtex entries for the modules of the User and Reference Manual, as well as for publications
- * directly related to the GUDHI library.
- * \section GudhiBibtex GUDHI bibtex
- * \verbinclude biblio/how_to_cite_gudhi.bib
-*/
diff --git a/doc/common/main_page.h b/doc/common/main_page.h
deleted file mode 100644
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--- a/doc/common/main_page.h
+++ /dev/null
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-/*! \mainpage The C++ library
- * \tableofcontents
- * \image html "Gudhi_banner.png" "" width=20cm
- *
- * \section Introduction Introduction
- * The GUDHI library (Geometry Understanding in Higher Dimensions) is a generic open source
- * <a class="el" target="_blank" href="http://gudhi.gforge.inria.fr/doc/latest/">C++ library</a> for
- * Computational Topology and Topological Data Analysis
- * (<a class="el" target="_blank" href="https://en.wikipedia.org/wiki/Topological_data_analysis">TDA</a>).
- * The GUDHI library intends to help the development of new algorithmic solutions in TDA and their transfer to
- * applications. It provides robust, efficient, flexible and easy to use implementations of state-of-the-art
- * algorithms and data structures.
- *
- * The current release of the GUDHI library includes:
- *
- * \li Data structures to represent, construct and manipulate simplicial complexes.
- * \li Simplification of simplicial complexes by edge contraction.
- * \li Algorithms to compute persistent homology and bottleneck distance.
- *
- * All data-structures are generic and several of their aspects can be parameterized via template classes.
- * We refer to \cite gudhilibrary_ICMS14 for a detailed description of the design of the library.
- *
- \section DataStructures Data structures
- \subsection AlphaComplexDataStructure Alpha complex
- \image html "alpha_complex_representation.png" "Alpha complex representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Vincent Rouvreau<br>
- <b>Introduced in:</b> GUDHI 1.3.0<br>
- <b>Copyright:</b> GPL v3<br>
- <b>Requires:</b> \ref cgal &ge; 4.7.0 and \ref eigen3
- </td>
- <td width="75%">
- Alpha_complex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.<br>
- The filtration value of each simplex is computed as the square of the circumradius of the simplex if the
- circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration
- values of the codimension 1 cofaces that make it not Gabriel otherwise.
- All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into
- the complex.<br>
- <b>User manual:</b> \ref alpha_complex - <b>Reference manual:</b> Gudhi::alpha_complex::Alpha_complex
- </td>
- </tr>
-</table>
- \subsection CechComplexDataStructure ÄŒech complex
- \image html "cech_complex_representation.png" "ÄŒech complex representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Vincent Rouvreau<br>
- <b>Introduced in:</b> GUDHI 2.2.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- The ÄŒech complex is a simplicial complex constructed from a proximity graph.<br>
- The set of all simplices is filtered by the radius of their minimal enclosing ball.<br>
- <b>User manual:</b> \ref cech_complex - <b>Reference manual:</b> Gudhi::cech_complex::Cech_complex
- </td>
- </tr>
-</table>
- \subsection CubicalComplexDataStructure Cubical complex
- \image html "Cubical_complex_representation.png" "Cubical complex representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Pawel Dlotko<br>
- <b>Introduced in:</b> GUDHI 1.3.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- The cubical complex is an example of a structured complex useful in computational mathematics (specially
- rigorous numerics) and image analysis.<br>
- <b>User manual:</b> \ref cubical_complex - <b>Reference manual:</b> Gudhi::cubical_complex::Bitmap_cubical_complex
- </td>
- </tr>
-</table>
- \subsection RipsComplexDataStructure Rips complex
- \image html "rips_complex_representation.png" "Rips complex representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Cl&eacute;ment Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse<br>
- <b>Introduced in:</b> GUDHI 2.0.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- Rips_complex is a simplicial complex constructed from a one skeleton graph.<br>
- The filtration value of each edge is computed from a user-given distance function and is inserted until a
- user-given threshold value.<br>
- This complex can be built from a point cloud and a distance function, or from a distance matrix.<br>
- <b>User manual:</b> \ref rips_complex - <b>Reference manual:</b> Gudhi::rips_complex::Rips_complex
- </td>
- </tr>
-</table>
- \subsection SimplexTreeDataStructure Simplex tree
- \image html "Simplex_tree_representation.png" "Simplex tree representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Cl&eacute;ment Maria<br>
- <b>Introduced in:</b> GUDHI 1.0.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- The simplex tree is an efficient and flexible
- data structure for representing general (filtered) simplicial complexes. The data structure
- is described in \cite boissonnatmariasimplextreealgorithmica .<br>
- <b>User manual:</b> \ref simplex_tree - <b>Reference manual:</b> Gudhi::Simplex_tree
- </td>
- </tr>
-</table>
- \subsection CoverComplexDataStructure Cover Complexes
- \image html "gicvisu.jpg" "Graph Induced Complex of a point cloud."
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Mathieu Carri&egrave;re<br>
- <b>Introduced in:</b> GUDHI 2.1.0<br>
- <b>Copyright:</b> GPL v3<br>
- <b>Requires:</b> \ref cgal &ge; 4.8.1
- </td>
- <td width="75%">
- Nerves and Graph Induced Complexes are cover complexes, i.e. simplicial complexes that provably contain
- topological information about the input data. They can be computed with a cover of the
- data, that comes i.e. from the preimage of a family of intervals covering the image
- of a scalar-valued function defined on the data. <br>
- <b>User manual:</b> \ref cover_complex - <b>Reference manual:</b> Gudhi::cover_complex::Cover_complex
- </td>
- </tr>
-</table>
- \subsection SkeletonBlockerDataStructure Skeleton blocker
- \image html "ds_representation.png" "Skeleton blocker representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> David Salinas<br>
- <b>Introduced in:</b> GUDHI 1.1.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- The Skeleton-Blocker data-structure proposes a light encoding for simplicial complexes by storing only an *implicit*
- representation of its simplices \cite socg_blockers_2011,\cite blockers2012. Intuitively, it just stores the
- 1-skeleton of a simplicial complex with a graph and the set of its "missing faces" that is very small in practice.
- This data-structure handles all simplicial complexes operations such as simplex enumeration or simplex removal but
- operations that are particularly efficient are operations that do not require simplex enumeration such as edge
- iteration, link computation or simplex contraction.<br>
- <b>User manual:</b> \ref skbl - <b>Reference manual:</b> Gudhi::skeleton_blocker::Skeleton_blocker_complex
- </td>
- </tr>
-</table>
- \subsection TangentialComplexDataStructure Tangential complex
- \image html "tc_examples.png" "Tangential complex representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Cl&eacute;ment Jamin<br>
- <b>Introduced in:</b> GUDHI 2.0.0<br>
- <b>Copyright:</b> GPL v3<br>
- <b>Requires:</b> \ref cgal &ge; 4.8.1 and \ref eigen3
- </td>
- <td width="75%">
- A Tangential Delaunay complex is a <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
- designed to reconstruct a \f$ k \f$-dimensional manifold embedded in \f$ d \f$-dimensional Euclidean space.
- The input is a point sample coming from an unknown manifold.
- The running time depends only linearly on the extrinsic dimension \f$ d \f$
- and exponentially on the intrinsic dimension \f$ k \f$.<br>
- <b>User manual:</b> \ref tangential_complex - <b>Reference manual:</b> Gudhi::tangential_complex::Tangential_complex
- </td>
- </tr>
-</table>
- \subsection WitnessComplexDataStructure Witness complex
- \image html "Witness_complex_representation.png" "Witness complex representation"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Siargey Kachanovich<br>
- <b>Introduced in:</b> GUDHI 1.3.0<br>
- <b>Copyright:</b> GPL v3<br>
- <b>Euclidean version requires:</b> \ref cgal &ge; 4.6.0 and \ref eigen3
- </td>
- <td width="75%">
- Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$.
- The data structure is described in \cite boissonnatmariasimplextreealgorithmica .<br>
- <b>User manual:</b> \ref witness_complex - <b>Reference manual:</b> Gudhi::witness_complex::SimplicialComplexForWitness
- </td>
- </tr>
-</table>
-
- \section Toolbox Toolbox
-
- \subsection BottleneckDistanceToolbox Bottleneck distance
- \image html "perturb_pd.png" "Bottleneck distance is the length of the longest edge"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Fran&ccedil;ois Godi<br>
- <b>Introduced in:</b> GUDHI 2.0.0<br>
- <b>Copyright:</b> GPL v3<br>
- <b>Requires:</b> \ref cgal &ge; 4.8.1
- </td>
- <td width="75%">
- Bottleneck distance measures the similarity between two persistence diagrams.
- It's the shortest distance b for which there exists a perfect matching between
- the points of the two diagrams (+ all the diagonal points) such that
- any couple of matched points are at distance at most b.
- <br>
- <b>User manual:</b> \ref bottleneck_distance
- </td>
- </tr>
-</table>
- \subsection ContractionToolbox Contraction
- \image html "sphere_contraction_representation.png" "Sphere contraction example"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> David Salinas<br>
- <b>Introduced in:</b> GUDHI 1.1.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- The purpose of this package is to offer a user-friendly interface for edge contraction simplification of huge
- simplicial complexes. It uses the \ref skbl data-structure whose size remains small during simplification of most
- used geometrical complexes of topological data analysis such as the Rips or the Delaunay complexes. In practice,
- the size of this data-structure is even much lower than the total number of simplices.<br>
- <b>User manual:</b> \ref contr
- </td>
- </tr>
-</table>
- \subsection PersistentCohomologyToolbox Persistent Cohomology
- \image html "3DTorus_poch.png" "Rips Persistent Cohomology on a 3D Torus"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Cl&eacute;ment Maria<br>
- <b>Introduced in:</b> GUDHI 1.0.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- The theory of homology consists in attaching to a topological space a sequence of (homology) groups, capturing
- global topological features like connected components, holes, cavities, etc. Persistent homology studies the
- evolution -- birth, life and death -- of these features when the topological space is changing. Consequently, the
- theory is essentially composed of three elements: topological spaces, their homology groups and an evolution
- scheme.
- Computation of persistent cohomology using the algorithm of \cite DBLP:journals/dcg/SilvaMV11 and
- \cite DBLP:journals/corr/abs-1208-5018 and the Compressed Annotation Matrix implementation of
- \cite DBLP:conf/esa/BoissonnatDM13 .<br>
- <b>User manual:</b> \ref persistent_cohomology - <b>Reference manual:</b> Gudhi::persistent_cohomology::Persistent_cohomology
- </td>
- </tr>
-</table>
- \subsection PersistenceRepresentationsToolbox Persistence representations
- \image html "average_landscape.png" "Persistence representations"
-<table border="0">
- <tr>
- <td width="25%">
- <b>Author:</b> Pawel Dlotko<br>
- <b>Introduced in:</b> GUDHI 2.1.0<br>
- <b>Copyright:</b> GPL v3<br>
- </td>
- <td width="75%">
- It contains implementation of various representations of persistence diagrams; diagrams themselves, persistence
- landscapes (rigorous and grid version), persistence heath maps, vectors and others. It implements basic
- functionalities which are neccessary to use persistence in statistics and machine learning.<br>
- <b>User manual:</b> \ref Persistence_representations
- </td>
- </tr>
-</table>
-
-*/
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