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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_ diff --git a/doc/Alpha_complex/alpha_complex_doc.ipe b/doc/Alpha_complex/alpha_complex_doc.ipe deleted file mode 100644 index 71e5ce6c..00000000 --- a/doc/Alpha_complex/alpha_complex_doc.ipe +++ /dev/null @@ -1,296 +0,0 @@ -<?xml version="1.0"?> -<!DOCTYPE ipe SYSTEM "ipe.dtd"> -<ipe version="70107" creator="Ipe 7.1.10"> -<info 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a/doc/Alpha_complex/alpha_complex_representation.png +++ /dev/null diff --git a/doc/Bitmap_cubical_complex/COPYRIGHT b/doc/Bitmap_cubical_complex/COPYRIGHT deleted file mode 100644 index 2b14dcb9..00000000 --- a/doc/Bitmap_cubical_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): 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. 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stroke="black" arrow="normal/normal"> -152 456 m -152 648 l -</path> -</page> -</ipe> diff --git a/doc/Bitmap_cubical_complex/Cubical_complex_representation.png b/doc/Bitmap_cubical_complex/Cubical_complex_representation.png Binary files differdeleted file mode 100644 index afb2a75e..00000000 --- a/doc/Bitmap_cubical_complex/Cubical_complex_representation.png +++ /dev/null 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 Binary files differdeleted file mode 100644 index 77167b13..00000000 --- a/doc/Bitmap_cubical_complex/bitmapAllCubes.png +++ /dev/null diff --git a/doc/Bitmap_cubical_complex/exampleBitmap.png b/doc/Bitmap_cubical_complex/exampleBitmap.png Binary files differdeleted file mode 100644 index 069c6eb2..00000000 --- a/doc/Bitmap_cubical_complex/exampleBitmap.png +++ /dev/null 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 François 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 Binary files differdeleted file mode 100644 index be638de0..00000000 --- a/doc/Bottleneck_distance/perturb_pd.png +++ /dev/null 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_ diff --git a/doc/Cech_complex/cech_complex_representation.ipe b/doc/Cech_complex/cech_complex_representation.ipe deleted file mode 100644 index 377745a3..00000000 --- a/doc/Cech_complex/cech_complex_representation.ipe +++ /dev/null @@ -1,330 +0,0 @@ -<?xml version="1.0"?> -<!DOCTYPE ipe SYSTEM "ipe.dtd"> -<ipe version="70107" creator="Ipe 7.1.10"> -<info created="D:20150603143945" modified="D:20180305162524"/> -<ipestyle name="basic"> -<symbol name="arrow/arc(spx)"> -<path 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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. 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x="141.32632" - y="304.69067">9 </tspan></text> - <text - xml:space="preserve" - style="font-size:4.58914995px;font-style:normal;font-weight:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans" - x="210.88516" - y="304.76022" - id="text4521" - sodipodi:linespacing="125%"><tspan - sodipodi:role="line" - id="tspan4523" - x="210.88516" - y="304.76022">3</tspan></text> - <text - xml:space="preserve" - style="font-size:6.70418215px;font-style:normal;font-weight:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans" - x="309.4176" - y="300.58682" - id="text4507-8" - sodipodi:linespacing="125%"><tspan - sodipodi:role="line" - x="309.4176" - y="300.58682" - id="tspan4515-4" - style="text-align:center;text-anchor:middle">Rips complex built uppon these points</tspan><tspan - sodipodi:role="line" - x="309.4176" - y="308.96704" - style="text-align:center;text-anchor:middle" - id="tspan4599">20 millions simplices</tspan><tspan - sodipodi:role="line" - x="309.4176" - y="317.34729" - id="tspan4511-3" - style="text-align:center;text-anchor:middle" /></text> - <text - xml:space="preserve" - style="font-size:6.70418215px;font-style:normal;font-weight:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans" - x="476.61395" - y="300.4592" - id="text4507-8-0" - sodipodi:linespacing="125%"><tspan - sodipodi:role="line" - x="476.61395" - y="300.4592" - id="tspan4511-3-9" - style="text-align:center;text-anchor:middle">Simplicial complex obtained after simplification</tspan><tspan - sodipodi:role="line" - x="476.61395" - y="308.83942" - style="text-align:center;text-anchor:middle" - id="tspan4601">714 simplices</tspan></text> - </g> -</svg> diff --git a/doc/Contraction/sphere_contraction_representation.png b/doc/Contraction/sphere_contraction_representation.png Binary files differdeleted file mode 100644 index edf37bf3..00000000 --- a/doc/Contraction/sphere_contraction_representation.png +++ /dev/null diff --git a/doc/Contraction/zoom.png b/doc/Contraction/zoom.png Binary files differdeleted file mode 100644 index 38d2b520..00000000 --- a/doc/Contraction/zoom.png +++ /dev/null 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 Binary files differdeleted file mode 100644 index cb1b9b7f..00000000 --- a/doc/Nerve_GIC/GIC.jpg +++ /dev/null diff --git a/doc/Nerve_GIC/GIC.pdf b/doc/Nerve_GIC/GIC.pdf Binary files differdeleted file mode 100644 index 30525745..00000000 --- a/doc/Nerve_GIC/GIC.pdf +++ /dev/null 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_ diff --git a/doc/Nerve_GIC/coordGICvisu.pdf b/doc/Nerve_GIC/coordGICvisu.pdf Binary files differdeleted file mode 100644 index 313aa1b5..00000000 --- a/doc/Nerve_GIC/coordGICvisu.pdf +++ /dev/null diff --git a/doc/Nerve_GIC/coordGICvisu2.jpg b/doc/Nerve_GIC/coordGICvisu2.jpg Binary files differdeleted file mode 100644 index 046feb2a..00000000 --- a/doc/Nerve_GIC/coordGICvisu2.jpg +++ /dev/null diff --git a/doc/Nerve_GIC/funcGICvisu.jpg b/doc/Nerve_GIC/funcGICvisu.jpg Binary files differdeleted file mode 100644 index 36b64dde..00000000 --- a/doc/Nerve_GIC/funcGICvisu.jpg +++ /dev/null diff --git a/doc/Nerve_GIC/funcGICvisu.pdf b/doc/Nerve_GIC/funcGICvisu.pdf Binary files differdeleted file mode 100644 index d7456cd3..00000000 --- a/doc/Nerve_GIC/funcGICvisu.pdf +++ /dev/null diff --git a/doc/Nerve_GIC/gicvisu.jpg b/doc/Nerve_GIC/gicvisu.jpg Binary files differdeleted file mode 100644 index 576dae47..00000000 --- a/doc/Nerve_GIC/gicvisu.jpg +++ /dev/null diff --git a/doc/Nerve_GIC/gicvoronoivisu.jpg b/doc/Nerve_GIC/gicvoronoivisu.jpg Binary files differdeleted file mode 100644 index cd86c411..00000000 --- a/doc/Nerve_GIC/gicvoronoivisu.jpg +++ /dev/null diff --git a/doc/Nerve_GIC/nerve.png b/doc/Nerve_GIC/nerve.png Binary files differdeleted file mode 100644 index b66da4a4..00000000 --- a/doc/Nerve_GIC/nerve.png +++ /dev/null diff --git a/doc/Nerve_GIC/nervevisu.jpg b/doc/Nerve_GIC/nervevisu.jpg Binary files differdeleted file mode 100644 index 67ae1d7e..00000000 --- a/doc/Nerve_GIC/nervevisu.jpg +++ /dev/null diff --git a/doc/Persistence_representations/Persistence_representations_doc.h b/doc/Persistence_representations/Persistence_representations_doc.h deleted file mode 100644 index 4d850a02..00000000 --- a/doc/Persistence_representations/Persistence_representations_doc.h +++ /dev/null @@ -1,259 +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) 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 diff --git a/doc/Persistence_representations/average_landscape.png b/doc/Persistence_representations/average_landscape.png Binary files differdeleted file mode 100644 index ea59926b..00000000 --- a/doc/Persistence_representations/average_landscape.png +++ /dev/null diff --git a/doc/Persistent_cohomology/3DTorus_poch.png b/doc/Persistent_cohomology/3DTorus_poch.png Binary files differdeleted file mode 100644 index 1c9d8328..00000000 --- a/doc/Persistent_cohomology/3DTorus_poch.png +++ /dev/null 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$. - * And so on for simplex (0,1,2,3). - * - * If the Rips_complex interfaces are not detailed enough for your need, please refer to - * <a href="_persistent_cohomology_2rips_persistence_step_by_step_8cpp-example.html"> - * rips_persistence_step_by_step.cpp</a> example, where the constructions of the graph and - * the Simplex_tree are more detailed. - * - * \section sparserips Sparse Rips complex - * - * Even truncated in filtration value and dimension, the Rips complex remains - * quite large. However, it is possible to approximate it by a much smaller - * filtered simplicial complex (linear size, with constants that depend on - * ε and the doubling dimension of the space) that is - * \f$(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 ε, 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 index 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a/doc/Simplex_tree/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/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 Clément 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 Binary files differdeleted file mode 100644 index 9d401520..00000000 --- a/doc/Simplex_tree/Simplex_tree_representation.png +++ /dev/null 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. 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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 Clément 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 Clément 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 González 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 Clément 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_ diff --git a/doc/Tangential_complex/tc_example_01.png b/doc/Tangential_complex/tc_example_01.png Binary files differdeleted file mode 100644 index 8afe6198..00000000 --- a/doc/Tangential_complex/tc_example_01.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_02.png b/doc/Tangential_complex/tc_example_02.png Binary files differdeleted file mode 100644 index 01591c1d..00000000 --- a/doc/Tangential_complex/tc_example_02.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_03.png b/doc/Tangential_complex/tc_example_03.png Binary files differdeleted file mode 100644 index 5de04e01..00000000 --- a/doc/Tangential_complex/tc_example_03.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_05.png b/doc/Tangential_complex/tc_example_05.png Binary files differdeleted file mode 100644 index fdd5e5fa..00000000 --- a/doc/Tangential_complex/tc_example_05.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_06.png b/doc/Tangential_complex/tc_example_06.png Binary files differdeleted file mode 100644 index 31ad3c43..00000000 --- a/doc/Tangential_complex/tc_example_06.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_07.png b/doc/Tangential_complex/tc_example_07.png Binary files differdeleted file mode 100644 index 47e34de7..00000000 --- a/doc/Tangential_complex/tc_example_07.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_07_after.png b/doc/Tangential_complex/tc_example_07_after.png Binary files differdeleted file mode 100644 index 981350d2..00000000 --- a/doc/Tangential_complex/tc_example_07_after.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_07_before.png b/doc/Tangential_complex/tc_example_07_before.png Binary files differdeleted file mode 100644 index ddc6bc7b..00000000 --- a/doc/Tangential_complex/tc_example_07_before.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_08.png b/doc/Tangential_complex/tc_example_08.png Binary files differdeleted file mode 100644 index 119a87de..00000000 --- a/doc/Tangential_complex/tc_example_08.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_example_09.png b/doc/Tangential_complex/tc_example_09.png Binary files differdeleted file mode 100644 index 31bac1e0..00000000 --- a/doc/Tangential_complex/tc_example_09.png +++ /dev/null diff --git a/doc/Tangential_complex/tc_examples.png b/doc/Tangential_complex/tc_examples.png Binary files differdeleted file mode 100644 index b6544afe..00000000 --- a/doc/Tangential_complex/tc_examples.png +++ /dev/null diff --git a/doc/Witness_complex/COPYRIGHT b/doc/Witness_complex/COPYRIGHT deleted file mode 100644 index 25a700cf..00000000 --- a/doc/Witness_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): 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 deleted file mode 100644 index 62203054..00000000 --- a/doc/Witness_complex/Witness_complex_doc.h +++ /dev/null @@ -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_ diff --git a/doc/Witness_complex/Witness_complex_representation.ipe b/doc/Witness_complex/Witness_complex_representation.ipe deleted file mode 100644 index f9c45d5d..00000000 --- a/doc/Witness_complex/Witness_complex_representation.ipe +++ /dev/null @@ -1,280 +0,0 @@ -<?xml version="1.0"?> -<!DOCTYPE ipe SYSTEM "ipe.dtd"> -<ipe 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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--> Version $projectnumber<!--END PROJECT_NUMBER--> -<!--BEGIN PROJECT_BRIEF--> - $projectbrief<!--END PROJECT_BRIEF--> -<!--BEGIN PROJECT_BRIEF--> - 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=" GUDHI"> 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> ≥ 1.48.0 - * and <a target="_blank" href="https://www.cmake.org/">CMake</a> ≥ 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 ≥ 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 ≥ 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 ≥ 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 ≥ 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® 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® TBB installed is recommended to parallelize and accelerate some GUDHI computations. - * - * The following examples/utilities are using Intel® 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 index db1e80ce..00000000 --- a/doc/common/main_page.h +++ /dev/null @@ -1,269 +0,0 @@ -/*! \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 ≥ 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> Clément 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> Clément 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 Carrière<br> - <b>Introduced in:</b> GUDHI 2.1.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Requires:</b> \ref cgal ≥ 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> Clément Jamin<br> - <b>Introduced in:</b> GUDHI 2.0.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Requires:</b> \ref cgal ≥ 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$.<br> - <b>User manual:</b> \ref tangential_complex - <b>Reference manual:</b> Gudhi::tangential_complex::Tangential_complex - </td> - </tr> -</table> - \subsection WitnessComplexDataStructure Witness complex - \image html "Witness_complex_representation.png" "Witness complex representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Siargey Kachanovich<br> - <b>Introduced in:</b> GUDHI 1.3.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Euclidean version requires:</b> \ref cgal ≥ 4.6.0 and \ref eigen3 - </td> - <td width="75%"> - Witness complex \f$ 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> François Godi<br> - <b>Introduced in:</b> GUDHI 2.0.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Requires:</b> \ref cgal ≥ 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> Clément 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> - -*/ diff --git a/doc/common/offline_header.html b/doc/common/offline_header.html deleted file mode 100644 index 6a02a895..00000000 --- a/doc/common/offline_header.html +++ /dev/null @@ -1,41 +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 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" /> -$extrastylesheet -</head> -<body> - - -<div id="top"><!-- do not remove this div, it is closed by doxygen! --> - -<!--BEGIN TITLEAREA--> -<div id="titlearea"> -<table cellspacing="0" cellpadding="0"> - <tbody> - <tr style="height: 30px;"> - <!--BEGIN DISABLE_INDEX--> - <!--BEGIN SEARCHENGINE--> - <td>$searchbox</td> - <!--END SEARCHENGINE--> - <!--END DISABLE_INDEX--> - </tr> - </tbody> -</table> -</div> -<!--END TITLEAREA--> -<!-- end header part --> diff --git a/doc/common/stylesheet.css b/doc/common/stylesheet.css deleted file mode 100644 index 1df177a4..00000000 --- a/doc/common/stylesheet.css +++ /dev/null @@ -1,1367 +0,0 @@ -/* The standard CSS for doxygen 1.8.6 */ - -body, table, div, p, dl { - font: 400 14px/22px Roboto,sans-serif; 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