diff options
| author | Gard Spreemann <gspreemann@gmail.com> | 2018-06-15 12:34:03 +0200 |
|---|---|---|
| committer | Gard Spreemann <gspreemann@gmail.com> | 2018-06-15 12:34:03 +0200 |
| commit | 41482b4260b4aff3d6803e340d5c94fbefb9af67 (patch) | |
| tree | 89eae43dcb3fd4ab040e96f3d5479427d8cd2c7f /doc | |
| parent | 41a1b8c2728e212c832c0384c8bb424139a247cf (diff) | |
| parent | c524232f734de875d69e2f190f01a6c976024368 (diff) | |
Merge branch 'upstream/latest' into dfsg/latest
Diffstat (limited to 'doc')
33 files changed, 1063 insertions, 157 deletions
diff --git a/doc/Alpha_complex/COPYRIGHT b/doc/Alpha_complex/COPYRIGHT index dbad2380..5f1d97cc 100644 --- a/doc/Alpha_complex/COPYRIGHT +++ b/doc/Alpha_complex/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Vincent Rouvreau -Copyright (C) 2015 INRIA +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 diff --git a/doc/Alpha_complex/Intro_alpha_complex.h b/doc/Alpha_complex/Intro_alpha_complex.h index a08663ca..7a375c9f 100644 --- a/doc/Alpha_complex/Intro_alpha_complex.h +++ b/doc/Alpha_complex/Intro_alpha_complex.h @@ -4,7 +4,7 @@ * * Author(s): Vincent Rouvreau * - * Copyright (C) 2015 INRIA + * 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 @@ -57,9 +57,13 @@ namespace alpha_complex { * 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 + * \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 @@ -89,63 +93,29 @@ namespace alpha_complex { * \image html "alpha_complex_doc.png" "Simplicial complex structure construction example" * * \subsection filtrationcomputation Filtration value computation algorithm - * - * - * - * <ul> - * <li style="list-style-type: none;">\f$ \textbf{for } i : dimension \rightarrow 0 \textbf{ do} \f$ - * <ul> - * <li style="list-style-type: none;">\f$\textbf{for all } \sigma of dimension i \f$ - * <ul> - * <li style="list-style-type: none;">\f$\textbf{if } filtration( \sigma ) is NaN \textbf{ then} \f$ - * <ul> - * <li style="list-style-type: none;">\f$ filtration( \sigma ) = \alpha^2( \sigma ) \f$ - * </li> - * </ul> - * </li> - * <li style="list-style-type: none;">\f$\textbf{end if}\f$ - * </li> - * <li style="list-style-type: none;">\f$\textbf{for all } \tau face of \sigma \textbf{ do} \f$ - * // propagate alpha filtration value - * <ul> - * <li style="list-style-type: none;">\f$\textbf{if } filtration( \tau ) is not NaN \textbf{ then} \f$ - * <ul> - * <li style="list-style-type: none;">\f$ filtration( \tau ) = min ( filtration( \tau ), filtration( \sigma ) ) \f$ - * </li> - * </ul> - * </li> - * <li style="list-style-type: none;">\f$\textbf{else}\f$ - * <ul> - * <li style="list-style-type: none;">\f$\textbf{if } \tau is not Gabriel for \sigma \textbf{ then} \f$ - * <ul> - * <li style="list-style-type: none;">\f$ filtration( \tau ) = filtration( \sigma ) \f$ - * </li> - * </ul> - * </li> - * <li style="list-style-type: none;">\f$\textbf{end if}\f$ - * </li> - * </ul> - * </li> - * <li style="list-style-type: none;">\f$\textbf{end if}\f$ - * </li> - * </ul> - * </li> - * <li style="list-style-type: none;">\f$\textbf{end for}\f$ - * </li> - * </ul> - * </li> - * <li style="list-style-type: none;">\f$\textbf{end for}\f$ - * </li> - * </ul> - * </li> - * <li style="list-style-type: none;">\f$\textbf{end for}\f$ - * </li> - * <li style="list-style-type: none;">\f$make\_filtration\_non\_decreasing()\f$ - * </li> - * <li style="list-style-type: none;">\f$prune\_above\_filtration()\f$ - * </li> - * </ul> - * + * <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 * diff --git a/doc/Bitmap_cubical_complex/COPYRIGHT b/doc/Bitmap_cubical_complex/COPYRIGHT index bcd46b23..2b14dcb9 100644 --- a/doc/Bitmap_cubical_complex/COPYRIGHT +++ b/doc/Bitmap_cubical_complex/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Pawel Dlotko -Copyright (C) 2015 INRIA +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 diff --git a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h index a5d7b60f..d1836ef0 100644 --- a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h +++ b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h @@ -4,7 +4,7 @@ * * Author(s): Pawel Dlotko * - * Copyright (C) 2015 INRIA Sophia-Saclay (France) + * 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 diff --git a/doc/Bottleneck_distance/COPYRIGHT b/doc/Bottleneck_distance/COPYRIGHT index 179740a6..1c2016b1 100644 --- a/doc/Bottleneck_distance/COPYRIGHT +++ b/doc/Bottleneck_distance/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): François Godi -Copyright (C) 2015 INRIA +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 diff --git a/doc/Bottleneck_distance/Intro_bottleneck_distance.h b/doc/Bottleneck_distance/Intro_bottleneck_distance.h index 3998fe8d..f8fce96c 100644 --- a/doc/Bottleneck_distance/Intro_bottleneck_distance.h +++ b/doc/Bottleneck_distance/Intro_bottleneck_distance.h @@ -4,7 +4,7 @@ * * Author: François Godi * - * Copyright (C) 2015 INRIA + * 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 diff --git a/doc/Cech_complex/COPYRIGHT b/doc/Cech_complex/COPYRIGHT new file mode 100644 index 00000000..5f1d97cc --- /dev/null +++ b/doc/Cech_complex/COPYRIGHT @@ -0,0 +1,19 @@ +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 new file mode 100644 index 00000000..4483bcb9 --- /dev/null +++ b/doc/Cech_complex/Intro_cech_complex.h @@ -0,0 +1,114 @@ +/* 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 Čech complex + * + * \author Vincent Rouvreau + * + * @{ + * + * \section cechdefinition Čech complex definition + * + * Čech 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" "Čech 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" "Čech 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 new file mode 100644 index 00000000..377745a3 --- /dev/null +++ b/doc/Cech_complex/cech_complex_representation.ipe @@ -0,0 +1,330 @@ +<?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 stroke="sym-stroke" 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files differnew file mode 100644 index 00000000..cc636616 --- /dev/null +++ b/doc/Cech_complex/cech_one_skeleton.png diff --git a/doc/Contraction/COPYRIGHT b/doc/Contraction/COPYRIGHT index 1de850d7..5b606ac2 100644 --- a/doc/Contraction/COPYRIGHT +++ b/doc/Contraction/COPYRIGHT @@ -3,7 +3,7 @@ The files of this directory are part of the Gudhi Library. The Gudhi library computational topology. Author(s): David Salinas -Copyright (C) 2015 INRIA +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 diff --git a/doc/Nerve_GIC/COPYRIGHT b/doc/Nerve_GIC/COPYRIGHT index 0c36a526..6b33053e 100644 --- a/doc/Nerve_GIC/COPYRIGHT +++ b/doc/Nerve_GIC/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Mathieu Carrière -Copyright (C) 2017 INRIA +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 diff --git a/doc/Nerve_GIC/Intro_graph_induced_complex.h b/doc/Nerve_GIC/Intro_graph_induced_complex.h index 2b648425..bc8aecc3 100644 --- a/doc/Nerve_GIC/Intro_graph_induced_complex.h +++ b/doc/Nerve_GIC/Intro_graph_induced_complex.h @@ -4,7 +4,7 @@ * * Author(s): Mathieu Carriere * - * Copyright (C) 2017 INRIA + * 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 diff --git a/doc/Persistence_representations/Persistence_representations_doc.h b/doc/Persistence_representations/Persistence_representations_doc.h index 38bd3a21..4d850a02 100644 --- a/doc/Persistence_representations/Persistence_representations_doc.h +++ b/doc/Persistence_representations/Persistence_representations_doc.h @@ -4,7 +4,7 @@ * * Author(s): Pawel Dlotko * - * Copyright (C) 2016 INRIA Sophia-Saclay (France) + * 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 diff --git a/doc/Persistent_cohomology/COPYRIGHT b/doc/Persistent_cohomology/COPYRIGHT index 34345bef..6cde9520 100644 --- a/doc/Persistent_cohomology/COPYRIGHT +++ b/doc/Persistent_cohomology/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Clément Maria -Copyright (C) 2015 INRIA +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 diff --git a/doc/Persistent_cohomology/Intro_persistent_cohomology.h b/doc/Persistent_cohomology/Intro_persistent_cohomology.h index 4dbe82c7..5fb9d4d2 100644 --- a/doc/Persistent_cohomology/Intro_persistent_cohomology.h +++ b/doc/Persistent_cohomology/Intro_persistent_cohomology.h @@ -4,7 +4,7 @@ * * Author(s): Clément Maria * - * Copyright (C) 2014 INRIA Sophia Antipolis-Méditerranée (France) + * 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 @@ -162,6 +162,19 @@ persistence diagram with a family of field coefficients. 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. diff --git a/doc/Rips_complex/COPYRIGHT b/doc/Rips_complex/COPYRIGHT index 594b7d03..2c31a0d6 100644 --- a/doc/Rips_complex/COPYRIGHT +++ b/doc/Rips_complex/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Clément Maria, Pawel Dlotko, Vincent Rouvreau -Copyright (C) 2015 INRIA +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 diff --git a/doc/Rips_complex/Intro_rips_complex.h b/doc/Rips_complex/Intro_rips_complex.h index 8c517516..712d3b6e 100644 --- a/doc/Rips_complex/Intro_rips_complex.h +++ b/doc/Rips_complex/Intro_rips_complex.h @@ -4,7 +4,7 @@ * * Author(s): Clément Maria, Pawel Dlotko, Vincent Rouvreau * - * Copyright (C) 2016 INRIA + * 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 @@ -29,28 +29,41 @@ namespace rips_complex { /** \defgroup rips_complex Rips complex * - * \author Clément Maria, Pawel Dlotko, Vincent Rouvreau + * \author Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse * * @{ * * \section ripsdefinition Rips complex definition * - * Rips_complex - * <a target="_blank" href="https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex">(Wikipedia)</a> is a - * one skeleton graph that allows to construct a - * <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a> - * from it. - * The input can be a point cloud with a given distance function, or a distance matrix. - * - * The filtration value of each edge is computed from a user-given distance function, or directly from the distance - * matrix. + * 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 + * Čech complex. After rescaling (Rips using the length of the edges and Čech + * 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. * - * All edges that have a filtration value strictly greater than a given threshold value are not inserted into - * the complex. + * The input can be given as a range of points and a distance function, or as a + * distance matrix. * - * When creating a simplicial complex from this one skeleton graph, Rips inserts the one skeleton graph into the data - * structure, and then expands the simplicial complex when required. - * * 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" @@ -61,7 +74,36 @@ namespace rips_complex { * * 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 graph construction over the Simplex_tree is more detailed. + * 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 * @@ -104,6 +146,24 @@ namespace rips_complex { * * \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 @@ -146,6 +206,33 @@ namespace rips_complex { * * \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 diff --git a/doc/Simplex_tree/COPYRIGHT b/doc/Simplex_tree/COPYRIGHT index 34345bef..6cde9520 100644 --- a/doc/Simplex_tree/COPYRIGHT +++ b/doc/Simplex_tree/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Clément Maria -Copyright (C) 2015 INRIA +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 diff --git a/doc/Simplex_tree/Intro_simplex_tree.h b/doc/Simplex_tree/Intro_simplex_tree.h index 6b80d1c9..db399489 100644 --- a/doc/Simplex_tree/Intro_simplex_tree.h +++ b/doc/Simplex_tree/Intro_simplex_tree.h @@ -4,7 +4,7 @@ * * Author(s): Clément Maria * - * Copyright (C) 2014 INRIA Sophia Antipolis-Méditerranée (France) + * 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 diff --git a/doc/Skeleton_blocker/COPYRIGHT b/doc/Skeleton_blocker/COPYRIGHT index 1de850d7..5b606ac2 100644 --- a/doc/Skeleton_blocker/COPYRIGHT +++ b/doc/Skeleton_blocker/COPYRIGHT @@ -3,7 +3,7 @@ The files of this directory are part of the Gudhi Library. The Gudhi library computational topology. Author(s): David Salinas -Copyright (C) 2015 INRIA +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 diff --git a/doc/Spatial_searching/Intro_spatial_searching.h b/doc/Spatial_searching/Intro_spatial_searching.h index 52ed65e4..f387ab2f 100644 --- a/doc/Spatial_searching/Intro_spatial_searching.h +++ b/doc/Spatial_searching/Intro_spatial_searching.h @@ -4,7 +4,7 @@ * * Author(s): Clement Jamin * - * Copyright (C) 2016 INRIA + * 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 diff --git a/doc/Subsampling/Intro_subsampling.h b/doc/Subsampling/Intro_subsampling.h index ab9cdc37..d88f6bf6 100644 --- a/doc/Subsampling/Intro_subsampling.h +++ b/doc/Subsampling/Intro_subsampling.h @@ -4,7 +4,7 @@ * * Author(s): Clement Jamin * - * Copyright (C) 2016 INRIA + * 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 diff --git a/doc/Tangential_complex/COPYRIGHT b/doc/Tangential_complex/COPYRIGHT index c4df0f64..f9f92471 100644 --- a/doc/Tangential_complex/COPYRIGHT +++ b/doc/Tangential_complex/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Clement Jamin -Copyright (C) 2015 INRIA +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 diff --git a/doc/Tangential_complex/Intro_tangential_complex.h b/doc/Tangential_complex/Intro_tangential_complex.h index 00e00c52..f4fc8ac7 100644 --- a/doc/Tangential_complex/Intro_tangential_complex.h +++ b/doc/Tangential_complex/Intro_tangential_complex.h @@ -4,7 +4,7 @@ * * Author(s): Clement Jamin * - * Copyright (C) 2016 INRIA + * 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 diff --git a/doc/Witness_complex/COPYRIGHT b/doc/Witness_complex/COPYRIGHT index 7d032c87..25a700cf 100644 --- a/doc/Witness_complex/COPYRIGHT +++ b/doc/Witness_complex/COPYRIGHT @@ -4,7 +4,7 @@ computational topology. Author(s): Siargey Kachanovich -Copyright (C) 2015 INRIA +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 diff --git a/doc/common/file_formats.h b/doc/common/file_formats.h index c60ed15a..523153b8 100644 --- a/doc/common/file_formats.h +++ b/doc/common/file_formats.h @@ -4,7 +4,7 @@ * * Author(s): Clément Jamin * -* Copyright (C) 2017 INRIA +* 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 diff --git a/doc/common/header.html b/doc/common/header.html index 9c514381..f8b13ec4 100644 --- a/doc/common/header.html +++ b/doc/common/header.html @@ -9,7 +9,7 @@ <!--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="http://pages.saclay.inria.fr/vincent.rouvreau/gudhi/gudhi-doc-2.0.0/assets/css/styles_feeling_responsive.css" /> +<link rel="stylesheet" type="text/css" href="http://gudhi.gforge.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> @@ -24,60 +24,61 @@ $extrastylesheet <!-- 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="http://gudhi.gforge.inria.fr" class="icon-tree"> GUDHI C++ library</a></h1> - </li> - <!-- Remove the class "menu-icon" to get rid of menu icon. 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It is a multi-platform library and compiles on Linux, Mac OSX and Visual Studio 2015. + * 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 demos Demos and examples * To build the demos and examples, run the following commands in a terminal: diff --git a/doc/common/main_page.h b/doc/common/main_page.h index b3e9ea03..db1e80ce 100644 --- a/doc/common/main_page.h +++ b/doc/common/main_page.h @@ -42,6 +42,22 @@ </td> </tr> </table> + \subsection CechComplexDataStructure Čech complex + \image html "cech_complex_representation.png" "Čech 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 Čech 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"> @@ -57,12 +73,13 @@ <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<br> + <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> @@ -75,7 +92,6 @@ </td> </tr> </table> -</table> \subsection SimplexTreeDataStructure Simplex tree \image html "Simplex_tree_representation.png" "Simplex tree representation" <table border="0"> diff --git a/doc/common/offline_header.html b/doc/common/offline_header.html new file mode 100644 index 00000000..6a02a895 --- /dev/null +++ b/doc/common/offline_header.html @@ -0,0 +1,41 @@ +<!-- 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 --> |
