From 8d7329f3e5ad843e553c3c5503cecc28ef2eead6 Mon Sep 17 00:00:00 2001 From: Gard Spreemann Date: Thu, 20 Apr 2017 11:10:45 +0200 Subject: GUDHI 2.0.0 as released by upstream in a tarball. --- doc/Alpha_complex/COPYRIGHT | 19 + doc/Alpha_complex/Intro_alpha_complex.h | 40 +- doc/Alpha_complex/alpha_complex_doc.ipe | 315 +---- doc/Alpha_complex/alpha_complex_doc.png | Bin 25554 -> 18720 bytes doc/Bitmap_cubical_complex/COPYRIGHT | 19 + .../Gudhi_Cubical_Complex_doc.h | 2 +- doc/Bottleneck_distance/COPYRIGHT | 19 + .../Intro_bottleneck_distance.h | 51 + doc/Bottleneck_distance/perturb_pd.png | Bin 0 -> 20864 bytes doc/Contraction/COPYRIGHT | 18 + doc/Persistent_cohomology/COPYRIGHT | 19 + .../Intro_persistent_cohomology.h | 44 +- doc/Rips_complex/COPYRIGHT | 19 + doc/Rips_complex/Intro_rips_complex.h | 158 +++ doc/Rips_complex/rips_complex_representation.ipe | 326 +++++ doc/Rips_complex/rips_complex_representation.png | Bin 0 -> 15677 bytes doc/Rips_complex/rips_one_skeleton.ipe | 326 +++++ doc/Rips_complex/rips_one_skeleton.png | Bin 0 -> 47651 bytes doc/Simplex_tree/COPYRIGHT | 19 + doc/Simplex_tree/Intro_simplex_tree.h | 7 +- doc/Skeleton_blocker/COPYRIGHT | 18 + doc/Spatial_searching/Intro_spatial_searching.h | 62 + doc/Subsampling/Intro_subsampling.h | 70 ++ doc/Tangential_complex/COPYRIGHT | 19 + doc/Tangential_complex/Intro_tangential_complex.h | 119 ++ doc/Tangential_complex/tc_example_01.png | Bin 0 -> 20323 bytes doc/Tangential_complex/tc_example_02.png | Bin 0 -> 36017 bytes doc/Tangential_complex/tc_example_03.png | Bin 0 -> 62990 bytes doc/Tangential_complex/tc_example_05.png | Bin 0 -> 36032 bytes doc/Tangential_complex/tc_example_06.png | Bin 0 -> 37195 bytes doc/Tangential_complex/tc_example_07.png | Bin 0 -> 49399 bytes doc/Tangential_complex/tc_example_07_after.png | Bin 0 -> 50132 bytes doc/Tangential_complex/tc_example_07_before.png | Bin 0 -> 48898 bytes doc/Tangential_complex/tc_example_08.png | Bin 0 -> 63636 bytes doc/Tangential_complex/tc_example_09.png | Bin 0 -> 35453 bytes doc/Tangential_complex/tc_examples.png | Bin 0 -> 150776 bytes doc/Witness_complex/COPYRIGHT | 19 + doc/Witness_complex/Witness_complex_doc.h | 105 +- .../Witness_complex_representation.ipe | 280 +++++ .../Witness_complex_representation.png | Bin 48899 -> 21202 bytes doc/Witness_complex/swit.svg | 1303 ++++++++++++++++++++ doc/common/header.html | 24 +- doc/common/main_page.h | 190 ++- doc/common/main_page.h~ | 341 ----- 44 files changed, 3223 insertions(+), 728 deletions(-) create mode 100644 doc/Alpha_complex/COPYRIGHT create mode 100644 doc/Bitmap_cubical_complex/COPYRIGHT create mode 100644 doc/Bottleneck_distance/COPYRIGHT create mode 100644 doc/Bottleneck_distance/Intro_bottleneck_distance.h create mode 100644 doc/Bottleneck_distance/perturb_pd.png create mode 100644 doc/Contraction/COPYRIGHT create mode 100644 doc/Persistent_cohomology/COPYRIGHT create mode 100644 doc/Rips_complex/COPYRIGHT create mode 100644 doc/Rips_complex/Intro_rips_complex.h create mode 100644 doc/Rips_complex/rips_complex_representation.ipe create mode 100644 doc/Rips_complex/rips_complex_representation.png create mode 100644 doc/Rips_complex/rips_one_skeleton.ipe create mode 100644 doc/Rips_complex/rips_one_skeleton.png create mode 100644 doc/Simplex_tree/COPYRIGHT create mode 100644 doc/Skeleton_blocker/COPYRIGHT create mode 100644 doc/Spatial_searching/Intro_spatial_searching.h create mode 100644 doc/Subsampling/Intro_subsampling.h create mode 100644 doc/Tangential_complex/COPYRIGHT create mode 100644 doc/Tangential_complex/Intro_tangential_complex.h create mode 100644 doc/Tangential_complex/tc_example_01.png create mode 100644 doc/Tangential_complex/tc_example_02.png create mode 100644 doc/Tangential_complex/tc_example_03.png create mode 100644 doc/Tangential_complex/tc_example_05.png create mode 100644 doc/Tangential_complex/tc_example_06.png create mode 100644 doc/Tangential_complex/tc_example_07.png create mode 100644 doc/Tangential_complex/tc_example_07_after.png create mode 100644 doc/Tangential_complex/tc_example_07_before.png create mode 100644 doc/Tangential_complex/tc_example_08.png create mode 100644 doc/Tangential_complex/tc_example_09.png create mode 100644 doc/Tangential_complex/tc_examples.png create mode 100644 doc/Witness_complex/COPYRIGHT create mode 100644 doc/Witness_complex/Witness_complex_representation.ipe create mode 100644 doc/Witness_complex/swit.svg delete mode 100644 doc/common/main_page.h~ (limited to 'doc') diff --git a/doc/Alpha_complex/COPYRIGHT b/doc/Alpha_complex/COPYRIGHT new file mode 100644 index 00000000..dbad2380 --- /dev/null +++ b/doc/Alpha_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 . diff --git a/doc/Alpha_complex/Intro_alpha_complex.h b/doc/Alpha_complex/Intro_alpha_complex.h index f3126169..69959fc5 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 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 @@ -39,7 +39,8 @@ namespace alpha_complex { * Alpha_complex is a simplicial complex * 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 + * 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 @@ -47,42 +48,45 @@ namespace alpha_complex { * * \image html "alpha_complex_representation.png" "Alpha-complex representation" * - * Alpha_complex is constructing a `Simplex_tree` using Delaunay Triangulation * \cite cgal:hdj-t-15b from CGAL (the Computational Geometry - * Algorithms Library \cite cgal:eb-15b). + * Algorithms Library \cite cgal:eb-15b) and is able to create a `SimplicialComplexForAlpha`. * * The complex is a template class requiring an Epick_d dD Geometry Kernel * \cite cgal:s-gkd-15b from CGAL as template parameter. * - * \remark When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex. + * \remark When the simplicial complex is constructed with an infinite value of alpha, the complex is a Delaunay + * complex. * * \section pointsexample Example from points * - * This example builds the Delaunay triangulation from the given points in a 2D static kernel, and initializes the - * alpha complex with it. + * 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 alpha complex. + * Then, it is asked to display information about the simplicial complex. * * \include Alpha_complex/Alpha_complex_from_points.cpp * * When launching: * - * \code $> ./alphapoints + * \code $> ./Alpha_complex_example_from_points * \endcode * * the program output is: * * \include Alpha_complex/alphaoffreader_for_doc_60.txt * - * \section algorithm Algorithm + * \section createcomplexalgorithm Create complex algorithm * * \subsection datastructure Data structure * - * In order to build the alpha complex, first, a Simplex tree is built from the cells of a Delaunay Triangulation. - * (The filtration value is set to NaN, which stands for unknown value): - * \image html "alpha_complex_doc.png" "Simplex tree structure construction example" + * 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 * @@ -129,12 +133,14 @@ namespace alpha_complex { * * \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 `Simplex_tree::make_filtration_non_decreasing()`. + * 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. `Simplex_tree::prune_above_filtration()`). + * 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. * * @@ -149,7 +155,7 @@ namespace alpha_complex { * * When launching: * - * \code $> ./alphaoffreader ../../data/points/alphacomplexdoc.off 32.0 + * \code $> ./Alpha_complex_example_from_off ../../data/points/alphacomplexdoc.off 32.0 * \endcode * * the program output is: diff --git a/doc/Alpha_complex/alpha_complex_doc.ipe b/doc/Alpha_complex/alpha_complex_doc.ipe index baf0d26a..71e5ce6c 100644 --- a/doc/Alpha_complex/alpha_complex_doc.ipe +++ b/doc/Alpha_complex/alpha_complex_doc.ipe @@ -1,7 +1,7 @@ - + @@ -278,35 +278,7 @@ h 320 580 l 280 660 l - -4 0 0 4 320 704 e - - -322.919 706.788 m -317.189 701.058 l -317.189 701.203 l - - -317.551 706.934 m -322.629 701.058 l - - -240 620 m -220 600 l - - -240 620 m -220 640 l - -Simplex tree structure - -280 630 m -170 630 l - - -280 610 m -170 610 l - +Simplicial complex data structure : @@ -314,282 +286,11 @@ h -2 - -300 688 m -300 676 l -312 676 l -312 688 l -h - -2 - -300 688 m -300 676 l -312 676 l -312 688 l -h - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -4 -1 - -300 688 m -300 676 l -312 676 l -312 688 l -h - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -4 -3 - -300 688 m -300 676 l -312 676 l -312 688 l -h - -2 - -300 688 m -300 676 l -312 676 l -312 688 l -h - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -3 -6 - -300 688 m -300 676 l -312 676 l -312 688 l -h - -4 - -300 688 m -300 676 l -312 676 l -312 688 l -h - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 -6 - -300 688 m -300 676 l -312 676 l -312 688 l -h - -5 - -300 688 m -300 676 l -312 676 l -312 688 l -h - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 - -292 716 m -292 728 l -316 728 l -316 716 l -h - - -316 716 m -316 728 l -340 728 l -340 716 l -h - - -340 716 m -340 728 l -364 728 l -364 716 l -h - - -364 716 m -364 728 l -388 728 l -388 716 l -h - - -388 716 m -388 728 l -412 728 l -412 716 l -h - - -412 716 m -412 728 l -436 728 l -436 716 l -h - - -436 716 m -436 728 l -460 728 l -460 716 l -h - -0 -1 -2 -3 -4 -5 -6 - -436 708 m -436 716 l - - -364 708 m -364 716 l - - -364 688 m -364 696 l - - -320 688 m -320 696 l - - -296 708 m -308 716 l -308 716 l - - -264 688 m -268 696 l - - -292 688 m -292 696 l - - -388 736 m -388 728 l - - -372 612 m -376 620 l - - -448 612 m -448 620 l - -3 - -300 688 m -300 676 l -312 676 l -312 688 l -h - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 - -364 688 m -364 696 l - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 - -436 708 m -436 716 l - - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 - -300 688 m -300 676 l -312 676 l -312 688 l -h - -6 - -436 708 m -436 716 l - +insert simplex and subfaces [0,1,2] +insert simplex and subfaces [1,2,3] +insert simplex and subfaces [0,2,4] +insert simplex and subfaces [2,3,6] +insert simplex and subfaces [2,4,6] +insert simplex and subfaces [4,5,6] diff --git a/doc/Alpha_complex/alpha_complex_doc.png b/doc/Alpha_complex/alpha_complex_doc.png index 0b6201da..170bae80 100644 Binary files a/doc/Alpha_complex/alpha_complex_doc.png and b/doc/Alpha_complex/alpha_complex_doc.png differ diff --git a/doc/Bitmap_cubical_complex/COPYRIGHT b/doc/Bitmap_cubical_complex/COPYRIGHT new file mode 100644 index 00000000..bcd46b23 --- /dev/null +++ b/doc/Bitmap_cubical_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): 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 . diff --git a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h index 4c9c04d9..5963caa3 100644 --- a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h +++ b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h @@ -63,7 +63,7 @@ namespace cubical_complex { * For further details and theory of cubical complexes, please consult \cite kaczynski2004computational as well as the * following paper \cite peikert2012topological . * - * \section datastructure Data structure. + * \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 diff --git a/doc/Bottleneck_distance/COPYRIGHT b/doc/Bottleneck_distance/COPYRIGHT new file mode 100644 index 00000000..179740a6 --- /dev/null +++ b/doc/Bottleneck_distance/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): 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 . diff --git a/doc/Bottleneck_distance/Intro_bottleneck_distance.h b/doc/Bottleneck_distance/Intro_bottleneck_distance.h new file mode 100644 index 00000000..3998fe8d --- /dev/null +++ b/doc/Bottleneck_distance/Intro_bottleneck_distance.h @@ -0,0 +1,51 @@ +/* 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 . + */ + +#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 new file mode 100644 index 00000000..be638de0 Binary files /dev/null and b/doc/Bottleneck_distance/perturb_pd.png differ diff --git a/doc/Contraction/COPYRIGHT b/doc/Contraction/COPYRIGHT new file mode 100644 index 00000000..1de850d7 --- /dev/null +++ b/doc/Contraction/COPYRIGHT @@ -0,0 +1,18 @@ +The files of this directory are part of the Gudhi Library. The Gudhi library +(Geometric Understanding in Higher Dimensions) is a generic C++ library for +computational topology. + +Author(s): David Salinas +Copyright (C) 2015 INRIA + +This program is free software: you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free Software +Foundation, either version 3 of the License, or (at your option) any later +version. + +This program is distributed in the hope that it will be useful, but WITHOUT +ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. + +You should have received a copy of the GNU General Public License along with +this program. If not, see . diff --git a/doc/Persistent_cohomology/COPYRIGHT b/doc/Persistent_cohomology/COPYRIGHT new file mode 100644 index 00000000..34345bef --- /dev/null +++ b/doc/Persistent_cohomology/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): 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 . diff --git a/doc/Persistent_cohomology/Intro_persistent_cohomology.h b/doc/Persistent_cohomology/Intro_persistent_cohomology.h index 0cba6361..e17e5926 100644 --- a/doc/Persistent_cohomology/Intro_persistent_cohomology.h +++ b/doc/Persistent_cohomology/Intro_persistent_cohomology.h @@ -139,22 +139,28 @@ namespace persistent_cohomology { by increasing filtration values (breaking ties so as a simplex appears after its subsimplices of same filtration value) provides an indexing scheme. -\section Examples +\section pcohexamples Examples We provide several example files: run these examples with -h for details on their use, and read the README file. \li -Persistent_cohomology/rips_persistence.cpp computes the Rips complex of a point cloud and its persistence diagram. +Persistent_cohomology/rips_persistence.cpp computes the Rips complex of a point cloud and outputs its persistence +diagram. +\code $> ./rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3 \endcode +\code The complex contains 177838 simplices + and has dimension 3 +3 0 0 inf +3 1 0.0983494 inf +3 1 0.104347 inf +3 2 0.138335 inf \endcode \li -Persistent_cohomology/rips_multifield_persistence.cpp computes the Rips complex of a point cloud and its +Persistent_cohomology/rips_multifield_persistence.cpp computes the Rips complex of a point cloud and outputs its persistence diagram with a family of field coefficients. -\li -Persistent_cohomology/performance_rips_persistence.cpp provides timings for the construction of the Rips complex -on a set of points sampling a Klein bottle in \f$\mathbb{R}^5\f$ with a simplex tree, its conversion to a -Hasse diagram and the computation of persistent homology and multi-field persistent homology for the -different representations. +\li +Persistent_cohomology/rips_distance_matrix_persistence.cpp computes the Rips complex of a distance matrix and +outputs its persistence diagram. \li Persistent_cohomology/alpha_complex_3d_persistence.cpp computes the persistent homology with @@ -166,6 +172,28 @@ Persistent_cohomology/alpha_complex_3d_persistence.cpp computes the persiste 2 1 0.0934117 1.00003 2 2 0.56444 1.03938 \endcode +\li +Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp 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 $> ./exact_alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off 2 0.1 \endcode +\code Simplex_tree dim: 3 +2 0 0 inf +2 2 0.0002 0.2028 \endcode + +\li +Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp computes the persistent homology with +\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the weighted alpha complex on points sampling from an OFF file +and a weights file. +\code $> ./weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off +../../data/points/tore3D_300.weights 2 0.45 \endcode +\code Simplex_tree dim: 3 +2 -0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 \endcode + \li Persistent_cohomology/alpha_complex_persistence.cpp computes the persistent homology with \f$\mathbb{Z}/p\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 new file mode 100644 index 00000000..594b7d03 --- /dev/null +++ b/doc/Rips_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): 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 . diff --git a/doc/Rips_complex/Intro_rips_complex.h b/doc/Rips_complex/Intro_rips_complex.h new file mode 100644 index 00000000..124dfec9 --- /dev/null +++ b/doc/Rips_complex/Intro_rips_complex.h @@ -0,0 +1,158 @@ +/* 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 . + */ + +#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 + * + * @{ + * + * \section ripsdefinition Rips complex definition + * + * Rips_complex + * (Wikipedia) is a + * one skeleton graph that allows to construct a + * simplicial complex + * 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. + * + * All edges that have a filtration value strictly greater than a given threshold value are not inserted into + * the complex. + * + * 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" + * + * 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 + * + * rips_persistence_step_by_step.cpp example, where the graph construction over the Simplex_tree is more detailed. + * + * \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 + * + * + * + * \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 + * + * \copyright GNU General Public License v3. + * \verbatim Contact: gudhi-users@lists.gforge.inria.fr \endverbatim + */ +/** @} */ // 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 new file mode 100644 index 00000000..7f6028f4 --- /dev/null +++ b/doc/Rips_complex/rips_complex_representation.ipe @@ -0,0 +1,326 @@ + + + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h + + + + + +-0.5 -0.5 m +0.5 -0.5 l +0.5 0.5 l +-0.5 0.5 l +h + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + + + +-0.43 -0.57 m +0.57 0.43 l +0.43 0.57 l +-0.57 -0.43 l +h + + +-0.43 0.57 m +0.57 -0.43 l +0.43 -0.57 l +-0.57 0.43 l +h + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 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a/doc/Rips_complex/rips_complex_representation.png b/doc/Rips_complex/rips_complex_representation.png new file mode 100644 index 00000000..e901d92e Binary files /dev/null and b/doc/Rips_complex/rips_complex_representation.png differ diff --git a/doc/Rips_complex/rips_one_skeleton.ipe b/doc/Rips_complex/rips_one_skeleton.ipe new file mode 100644 index 00000000..3a35970c --- /dev/null +++ b/doc/Rips_complex/rips_one_skeleton.ipe @@ -0,0 +1,326 @@ + + + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h + + + + + +-0.5 -0.5 m +0.5 -0.5 l +0.5 0.5 l +-0.5 0.5 l +h + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + + + +-0.43 -0.57 m +0.57 0.43 l +0.43 0.57 l +-0.57 -0.43 l +h + + +-0.43 0.57 m +0.57 -0.43 l +0.43 -0.57 l +-0.57 0.43 l +h + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +109.771 601.912 m +159.595 601.797 l +140.058 541.915 l +h + + +79.8776 552.169 m +109.756 601.699 l +139.812 542.209 l +h + + +69.8453 682.419 m +159.925 712.208 l +90.12 732.039 l +h + +One skeleton graph +0 +1 +2 +3 +4 +5 +6 + +60 710 m +40 660 l + + +40 660 m +130 690 l + + +130 690 m +60 710 l + + +40 660 m +80 580 l + + +80 580 m +130 580 l +130 580 l + + +130 580 m +110 520 l + + +110 520 m +50 530 l +50 530 l +50 530 l + + +50 530 m +80 580 l + + +130 580 m +130 690 l + + + + + + + +150.038 609.9 m +179.929 549.727 l + + + + +158.7 593.269 m +81.4925 544.805 l + + +256.324 639.958 m +370.055 639.958 l + + +56.8567 0 0 56.8567 313.217 639.756 e + + + +Rips threshold + + diff --git a/doc/Rips_complex/rips_one_skeleton.png b/doc/Rips_complex/rips_one_skeleton.png new file mode 100644 index 00000000..1028770e Binary files /dev/null and b/doc/Rips_complex/rips_one_skeleton.png differ diff --git a/doc/Simplex_tree/COPYRIGHT b/doc/Simplex_tree/COPYRIGHT new file mode 100644 index 00000000..34345bef --- /dev/null +++ b/doc/Simplex_tree/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): 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 . diff --git a/doc/Simplex_tree/Intro_simplex_tree.h b/doc/Simplex_tree/Intro_simplex_tree.h index ddf9ad22..940dd694 100644 --- a/doc/Simplex_tree/Intro_simplex_tree.h +++ b/doc/Simplex_tree/Intro_simplex_tree.h @@ -28,6 +28,7 @@ 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 @@ -65,8 +66,8 @@ Expand the simplex tree in 3.8e-05 s. Information of the Simplex Tree: Number of vertices = 10 Number of simplices = 98 \endcode * - * \li - * Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp - Simplex tree is computed and displayed from a 3D alpha + * \li + * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp - Simplex tree is computed and displayed from a 3D alpha * complex (Requires CGAL, GMP and GMPXX to be installed) * * @@ -76,7 +77,7 @@ Number of vertices = 10 Number of simplices = 98 \endcode * compact and harder to construct from scratch. * * \copyright GNU General Public License v3. - * @{ + * @} */ } // namespace Gudhi diff --git a/doc/Skeleton_blocker/COPYRIGHT b/doc/Skeleton_blocker/COPYRIGHT new file mode 100644 index 00000000..1de850d7 --- /dev/null +++ b/doc/Skeleton_blocker/COPYRIGHT @@ -0,0 +1,18 @@ +The files of this directory are part of the Gudhi Library. The Gudhi library +(Geometric Understanding in Higher Dimensions) is a generic C++ library for +computational topology. + +Author(s): David Salinas +Copyright (C) 2015 INRIA + +This program is free software: you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free Software +Foundation, either version 3 of the License, or (at your option) any later +version. + +This program is distributed in the hope that it will be useful, but WITHOUT +ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. + +You should have received a copy of the GNU General Public License along with +this program. If not, see . diff --git a/doc/Spatial_searching/Intro_spatial_searching.h b/doc/Spatial_searching/Intro_spatial_searching.h new file mode 100644 index 00000000..23705378 --- /dev/null +++ b/doc/Spatial_searching/Intro_spatial_searching.h @@ -0,0 +1,62 @@ +/* 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 . + */ + +#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 + * CGAL dD spatial searching algorithms. + * 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 + * CGAL documentation + * is highly recommended. + * + * \section spatial_searching_examples Example + * + * This example generates 500 random points, then performs queries for nearest and farthest points using different methods. + * + * \include Spatial_searching/example_spatial_searching.cpp + * + * \copyright GNU General Public License v3. + * \verbatim Contact: gudhi-users@lists.gforge.inria.fr \endverbatim + */ +/** @} */ // 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 new file mode 100644 index 00000000..c84616dd --- /dev/null +++ b/doc/Subsampling/Intro_subsampling.h @@ -0,0 +1,70 @@ +/* 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 . + */ + +#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 + * \copyright GNU General Public License v3. + * \verbatim Contact: gudhi-users@lists.gforge.inria.fr \endverbatim + */ +/** @} */ // 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 new file mode 100644 index 00000000..c4df0f64 --- /dev/null +++ b/doc/Tangential_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): 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 . diff --git a/doc/Tangential_complex/Intro_tangential_complex.h b/doc/Tangential_complex/Intro_tangential_complex.h new file mode 100644 index 00000000..3d687c1d --- /dev/null +++ b/doc/Tangential_complex/Intro_tangential_complex.h @@ -0,0 +1,119 @@ +/* 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 . + */ + +#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 simplicial complex +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 + +\copyright GNU General Public License v3. +\verbatim Contact: gudhi-users@lists.gforge.inria.fr \endverbatim + */ +/** @} */ // 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 new file mode 100644 index 00000000..8afe6198 Binary files /dev/null and b/doc/Tangential_complex/tc_example_01.png differ diff --git a/doc/Tangential_complex/tc_example_02.png b/doc/Tangential_complex/tc_example_02.png new file mode 100644 index 00000000..01591c1d Binary files /dev/null and b/doc/Tangential_complex/tc_example_02.png differ diff --git a/doc/Tangential_complex/tc_example_03.png b/doc/Tangential_complex/tc_example_03.png new file mode 100644 index 00000000..5de04e01 Binary files /dev/null and b/doc/Tangential_complex/tc_example_03.png differ diff --git a/doc/Tangential_complex/tc_example_05.png b/doc/Tangential_complex/tc_example_05.png new file mode 100644 index 00000000..fdd5e5fa Binary files /dev/null and b/doc/Tangential_complex/tc_example_05.png differ diff --git a/doc/Tangential_complex/tc_example_06.png b/doc/Tangential_complex/tc_example_06.png new file mode 100644 index 00000000..31ad3c43 Binary files /dev/null and b/doc/Tangential_complex/tc_example_06.png differ diff --git a/doc/Tangential_complex/tc_example_07.png b/doc/Tangential_complex/tc_example_07.png new file mode 100644 index 00000000..47e34de7 Binary files /dev/null and b/doc/Tangential_complex/tc_example_07.png differ diff --git a/doc/Tangential_complex/tc_example_07_after.png b/doc/Tangential_complex/tc_example_07_after.png new file mode 100644 index 00000000..981350d2 Binary files /dev/null and b/doc/Tangential_complex/tc_example_07_after.png differ diff --git a/doc/Tangential_complex/tc_example_07_before.png b/doc/Tangential_complex/tc_example_07_before.png new file mode 100644 index 00000000..ddc6bc7b Binary files /dev/null and b/doc/Tangential_complex/tc_example_07_before.png differ diff --git a/doc/Tangential_complex/tc_example_08.png b/doc/Tangential_complex/tc_example_08.png new file mode 100644 index 00000000..119a87de Binary files /dev/null and b/doc/Tangential_complex/tc_example_08.png differ diff --git a/doc/Tangential_complex/tc_example_09.png b/doc/Tangential_complex/tc_example_09.png new file mode 100644 index 00000000..31bac1e0 Binary files /dev/null and b/doc/Tangential_complex/tc_example_09.png differ diff --git a/doc/Tangential_complex/tc_examples.png b/doc/Tangential_complex/tc_examples.png new file mode 100644 index 00000000..b6544afe Binary files /dev/null and b/doc/Tangential_complex/tc_examples.png differ diff --git a/doc/Witness_complex/COPYRIGHT b/doc/Witness_complex/COPYRIGHT new file mode 100644 index 00000000..7d032c87 --- /dev/null +++ b/doc/Witness_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): 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 . diff --git a/doc/Witness_complex/Witness_complex_doc.h b/doc/Witness_complex/Witness_complex_doc.h index 60dfd27b..171a185f 100644 --- a/doc/Witness_complex/Witness_complex_doc.h +++ b/doc/Witness_complex/Witness_complex_doc.h @@ -8,31 +8,106 @@ \image html "Witness_complex_representation.png" "Witness complex representation" - \section Definitions + \section witnessdefinitions Definitions - Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$: + 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$L \subseteq W\f$ set of **landmarks**. + \li \f$L\f$ set of **landmarks**. - The simplices are based on landmarks - and a simplex belongs to the witness complex if and only if it is witnessed, that is: + Even though often the set of landmarks \f$L\f$ is a subset of the set of witnesses \f$ W\f$, it is not a requirement for the current implementation. - \f$ \sigma \subset L \f$ is witnessed if there exists a point \f$w \in W\f$ such that - w is closer to the vertices of \f$ \sigma \f$ than other points in \f$ L \f$ and all of its faces are witnessed as well. - - The data structure is described in \cite boissonnatmariasimplextreealgorithmica . + Landmarks are the vertices of the simplicial complex + and witnesses help to decide on which simplices are inserted via a predicate "is witnessed". - \section Implementation + De Silva and Carlsson in their paper \cite de2004topological differentiate **weak witnessing** and **strong witnessing**: - The principal class of this module is Gudhi::Witness_complex. + - *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$ - In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a witness and consists of landmarks sorted by distance to this witness. - This table can be constructed by two additional classes Landmark_choice_by_furthest_point and Landmark_choice_by_random_point also included in the module. + where \f$ d(.,.) \f$ is a distance function. - *\image html "bench_Cy8.png" "Running time as function on number of landmarks" width=10cm - *\image html "bench_sphere.png" "Running time as function on number of witnesses for |L|=300" width=10cm + 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 +#include +#include +#include + +#include + +#include +#include + +typedef CGAL::Epick_d K; +typedef typename K::Point_d Point_d; +typedef typename Gudhi::witness_complex::Euclidean_witness_complex 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 off_reader(file_name); + point_vector = Point_vector(off_reader.get_point_cloud()); + + // Choose landmarks + Gudhi::subsampling::pick_n_random_points(point_vector, nbL, 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/example_strong_witness_persistence.cpp \copyright GNU General Public License v3. diff --git a/doc/Witness_complex/Witness_complex_representation.ipe b/doc/Witness_complex/Witness_complex_representation.ipe new file mode 100644 index 00000000..f9c45d5d --- /dev/null +++ b/doc/Witness_complex/Witness_complex_representation.ipe @@ -0,0 +1,280 @@ + + + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h + + + + + +-0.5 -0.5 m +0.5 -0.5 l +0.5 0.5 l +-0.5 0.5 l +h + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + + + +-0.43 -0.57 m +0.57 0.43 l +0.43 0.57 l +-0.57 -0.43 l +h + + +-0.43 0.57 m +0.57 -0.43 l +0.43 -0.57 l +-0.57 0.43 l +h + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +48.8262 0 0 48.8262 288 672 e + +$\omega$ + +284 720 m +280 624 l +268 648 l +h + + + + +$\sigma$ + + + + + + + + + diff --git a/doc/Witness_complex/Witness_complex_representation.png b/doc/Witness_complex/Witness_complex_representation.png index 1d31a490..16e0504e 100644 Binary files a/doc/Witness_complex/Witness_complex_representation.png and b/doc/Witness_complex/Witness_complex_representation.png differ diff --git a/doc/Witness_complex/swit.svg b/doc/Witness_complex/swit.svg new file mode 100644 index 00000000..6ffb5fff --- /dev/null +++ b/doc/Witness_complex/swit.svg @@ -0,0 +1,1303 @@ + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/common/header.html b/doc/common/header.html index a6f3ed9c..53b5c0a2 100644 --- a/doc/common/header.html +++ b/doc/common/header.html @@ -9,7 +9,7 @@ $projectname: $title $title - + @@ -25,6 +25,13 @@ $extrastylesheet - +
diff --git a/doc/common/main_page.h b/doc/common/main_page.h index 0983051d..2e45e5aa 100644 --- a/doc/common/main_page.h +++ b/doc/common/main_page.h @@ -3,7 +3,9 @@ * \image html "Gudhi_banner.png" "" width=20cm * * \section Introduction Introduction - * The Gudhi library (Geometry Understanding in Higher Dimensions) is a generic open source C++ library for + * The GUDHI library (Geometry Understanding in Higher Dimensions) is a generic open source + * C++ library, with a + * Python interface, for * Computational Topology and Topological Data Analysis * (TDA). * The GUDHI library intends to help the development of new algorithmic solutions in TDA and their transfer to @@ -28,6 +30,7 @@ Author: Vincent Rouvreau
Introduced in: GUDHI 1.3.0
Copyright: GPL v3
+ Requires: \ref cgal ≥ 4.7.0 and \ref eigen3 Alpha_complex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.
@@ -55,6 +58,24 @@ User manual: \ref cubical_complex - Reference manual: Gudhi::cubical_complex::Bitmap_cubical_complex + \subsection RipsComplexDataStructure Rips complex + \image html "rips_complex_representation.png" "Rips complex representation" + + + + + +
+ Author: Clément Maria, Pawel Dlotko, Vincent Rouvreau
+ Introduced in: GUDHI 2.0.0
+ Copyright: GPL v3
+ 		+ Rips_complex is a simplicial complex constructed from a one skeleton graph.
+ The filtration value of each edge is computed from a user-given distance function and is inserted until a + user-given threshold value.
+ This complex can be built from a point cloud and a distance function, or from a distance matrix.
+ User manual: \ref rips_complex - Reference manual: Gudhi::rips_complex::Rips_complex +
\subsection SimplexTreeDataStructure Simplex tree \image html "Simplex_tree_representation.png" "Simplex tree representation" @@ -92,6 +113,26 @@ User manual: \ref skbl - Reference manual: Gudhi::skeleton_blocker::Skeleton_blocker_complex + + \subsection TangentialComplexDataStructure Tangential complex + \image html "tc_examples.png" "Tangential complex representation" + + + + +
+ Author: Clément Jamin
+ Introduced in: GUDHI 2.0.0
+ Copyright: GPL v3
+ Requires: \ref cgal ≥ 4.8.1 and \ref eigen3 + 		+ A Tangential Delaunay complex is a simplicial complex + 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$.
+ User manual: \ref tangential_complex - Reference manual: Gudhi::tangential_complex::Tangential_complex +
\subsection WitnessComplexDataStructure Witness complex \image html "Witness_complex_representation.png" "Witness complex representation" @@ -101,6 +142,7 @@ Author: Siargey Kachanovich
Introduced in: GUDHI 1.3.0
Copyright: GPL v3
+ Euclidean version requires: \ref cgal ≥ 4.6.0 and \ref eigen3 Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$. @@ -111,6 +153,26 @@ \section Toolbox Toolbox + \subsection BottleneckDistanceToolbox Bottleneck distance + \image html "perturb_pd.png" "Bottleneck distance is the length of the longest edge" + + + + + +
+ Author: François Godi
+ Introduced in: GUDHI 2.0.0
+ Copyright: GPL v3
+ Requires: \ref cgal ≥ 4.8.1 and \ref eigen3 + 		+ 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. +
+ User manual: \ref bottleneck_distance +
\subsection ContractionToolbox Contraction \image html "sphere_contraction_representation.png" "Sphere contraction example" @@ -153,11 +215,11 @@
*/ -/*! \page installation Gudhi installation +/*! \page installation GUDHI installation * \tableofcontents - * As Gudhi is a header only library, there is no need to install the library. + * 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 demos. + * Examples of GUDHI headers inclusion can be found in \ref demos. * * \section compiling Compiling * The library uses c++11 and requires Boost with version 1.48.0 or @@ -176,39 +238,54 @@ make \endverbatim * To test your build, run the following command in a terminal: * \verbatim make test \endverbatim * + * \subsection documentationgeneration Documentation + * To generate the documentation, Doxygen 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 + * * \section optionallibrary Optional third-party library - * \subsection gmp GMP: + * \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 GNU Multiple Precision Arithmetic * Library (GMP) and will not be built if GMP is not installed: - * \li - * Persistent_cohomology/performance_rips_persistence.cpp * \li * Persistent_cohomology/rips_multifield_persistence.cpp * * Having GMP version 4.2 or higher installed is recommended. * - * \subsection cgal CGAL: - * The \ref alpha_complex data structure and few examples requires CGAL, which is a C++ library which provides easy - * access to efficient and reliable geometric algorithms. + * \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 cmake . && make CGAL (or even + * cmake -DCGAL_HEADER_ONLY=ON . for CGAL version ≥ 4.8.0), thereafter you will be able to compile + * GUDHI by calling cmake -DCGAL_DIR=/your/path/to/CGAL-X.Y .. && make * - * Having CGAL version 4.4 or higher installed is recommended. The procedure to install this library according to + * 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 require the Computational Geometry Algorithms * Library (CGAL \cite cgal:eb-15b) and will not be built if CGAL is not installed: * \li * Persistent_cohomology/alpha_complex_3d_persistence.cpp - * \li - * Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp + * \li + * Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp + * \li + * Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp + * \li + * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp * - * The following example requires CGAL version ≥ 4.6: + * The following example requires CGAL version ≥ 4.6.0: * \li * Witness_complex/witness_complex_sphere.cpp * - * The following example requires CGAL version ≥ 4.7: + * The following example requires CGAL version ≥ 4.7.0: * \li * Alpha_complex/Alpha_complex_from_off.cpp * \li @@ -220,7 +297,29 @@ make \endverbatim * \li * Persistent_cohomology/custom_persistence_sort.cpp * - * \subsection eigen3 Eigen3: + * The following example requires CGAL version ≥ 4.8.1: + * \li + * Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp.cpp + * \li + * Bottleneck_distance/bottleneck_basic_example.cpp + * \li + * Bottleneck_distance/bottleneck_read_file_example.cpp + * \li + * Spatial_searching/example_spatial_searching.cpp + * \li + * Subsampling/example_choose_n_farthest_points.cpp + * \li + * Subsampling/example_custom_kernel.cpp + * \li + * Subsampling/example_pick_n_random_points.cpp + * \li + * Subsampling/example_sparsify_point_set.cpp + * \li + * Tangential_complex/example_basic.cpp + * \li + * Tangential_complex/example_with_perturb.cpp + * + * \subsection eigen3 Eigen3 * The \ref alpha_complex data structure and few examples requires * Eigen3 is a C++ template library for linear algebra: * matrices, vectors, numerical solvers, and related algorithms. @@ -228,9 +327,9 @@ make \endverbatim * The following example requires the Eigen3 and will not be * built if Eigen3 is not installed: * \li - * Alpha_complex/Alpha_complex_from_off.cpp (requires also Eigen3) + * Alpha_complex/Alpha_complex_from_off.cpp * \li - * Alpha_complex/Alpha_complex_from_points.cpp (requires also Eigen3) + * Alpha_complex/Alpha_complex_from_points.cpp * \li * Persistent_cohomology/alpha_complex_persistence.cpp * \li @@ -238,7 +337,7 @@ make \endverbatim * \li * Persistent_cohomology/custom_persistence_sort.cpp * - * \subsection tbb Threading Building Blocks: + * \subsection tbb Threading Building Blocks * Intel® TBB 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. @@ -262,8 +361,8 @@ make \endverbatim * Persistent_cohomology/alpha_complex_persistence.cpp * \li * Simplex_tree/simple_simplex_tree.cpp - * \li - * Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp + * \li + * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp * \li * Simplex_tree/simplex_tree_from_cliques_of_graph.cpp * \li @@ -272,28 +371,38 @@ make \endverbatim * Persistent_cohomology/alpha_complex_persistence.cpp * \li * Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp - * \li - * Persistent_cohomology/performance_rips_persistence.cpp * \li * Persistent_cohomology/persistence_from_file.cpp * \li * Persistent_cohomology/persistence_from_simple_simplex_tree.cpp * \li * Persistent_cohomology/plain_homology.cpp + * \li + * Persistent_cohomology/rips_distance_matrix_persistence.cpp * \li * Persistent_cohomology/rips_multifield_persistence.cpp * \li * Persistent_cohomology/rips_persistence.cpp + * \li + * Persistent_cohomology/rips_persistence_step_by_step.cpp + * \li + * Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp + * \li + * Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp * \li * Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp * \li * Persistent_cohomology/custom_persistence_sort.cpp + * \li + * Rips_complex/example_one_skeleton_rips_from_points.cpp + * \li + * Rips_complex/example_rips_complex_from_off_file.cpp * * \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. + * GUDHI is open to external contributions. If you want to join our development team, please contact us. * */ @@ -308,36 +417,55 @@ make \endverbatim * \verbinclude biblio/how_to_cite_gudhi.bib */ -// List of Gudhi examples - Doxygen needs at least a file tag to analyse comments +// List of GUDHI examples - Doxygen needs at least a file tag to analyse comments /*! @file Examples * @example Alpha_complex/Alpha_complex_from_off.cpp * @example Alpha_complex/Alpha_complex_from_points.cpp + * @example Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp + * @example Bottleneck_distance/bottleneck_basic_example.cpp + * @example Bottleneck_distance/bottleneck_read_file_example.cpp * @example Bitmap_cubical_complex/Bitmap_cubical_complex.cpp * @example Bitmap_cubical_complex/Bitmap_cubical_complex_periodic_boundary_conditions.cpp * @example Bitmap_cubical_complex/Random_bitmap_cubical_complex.cpp - * @example common/CGAL_3D_points_off_reader.cpp - * @example common/CGAL_points_off_reader.cpp + * @example common/example_CGAL_3D_points_off_reader.cpp + * @example common/example_CGAL_points_off_reader.cpp * @example Contraction/Garland_heckbert.cpp * @example Contraction/Rips_contraction.cpp * @example Persistent_cohomology/alpha_complex_3d_persistence.cpp * @example Persistent_cohomology/alpha_complex_persistence.cpp * @example Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp - * @example Persistent_cohomology/performance_rips_persistence.cpp + * @example Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp + * @example Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp * @example Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp * @example Persistent_cohomology/persistence_from_file.cpp * @example Persistent_cohomology/persistence_from_simple_simplex_tree.cpp * @example Persistent_cohomology/plain_homology.cpp * @example Persistent_cohomology/rips_multifield_persistence.cpp + * @example Persistent_cohomology/rips_distance_matrix_persistence.cpp * @example Persistent_cohomology/rips_persistence.cpp * @example Persistent_cohomology/custom_persistence_sort.cpp + * @example Persistent_cohomology/rips_persistence_step_by_step.cpp + * @example Rips_complex/example_one_skeleton_rips_from_points.cpp + * @example Rips_complex/example_rips_complex_from_off_file.cpp * @example Simplex_tree/mini_simplex_tree.cpp * @example Simplex_tree/simple_simplex_tree.cpp - * @example Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp + * @example Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp * @example Simplex_tree/simplex_tree_from_cliques_of_graph.cpp * @example Skeleton_blocker/Skeleton_blocker_from_simplices.cpp * @example Skeleton_blocker/Skeleton_blocker_iteration.cpp * @example Skeleton_blocker/Skeleton_blocker_link.cpp - * @example Witness_complex/witness_complex_from_file.cpp - * @example Witness_complex/witness_complex_sphere.cpp + * @example Spatial_searching/example_spatial_searching.cpp + * @example Subsampling/example_choose_n_farthest_points.cpp + * @example Subsampling/example_custom_kernel.cpp + * @example Subsampling/example_pick_n_random_points.cpp + * @example Subsampling/example_sparsify_point_set.cpp + * @example Tangential_complex/example_basic.cpp + * @example Tangential_complex/example_with_perturb.cpp + * @example Witness_complex/example_nearest_landmark_table.cpp + * @example Witness_complex/example_strong_witness_complex_off.cpp + * @example Witness_complex/example_strong_witness_persistence.cpp + * @example Witness_complex/example_witness_complex_off.cpp + * @example Witness_complex/example_witness_complex_persistence.cpp + * @example Witness_complex/example_witness_complex_sphere.cpp */ diff --git a/doc/common/main_page.h~ b/doc/common/main_page.h~ deleted file mode 100644 index abe7398b..00000000 --- a/doc/common/main_page.h~ +++ /dev/null @@ -1,341 +0,0 @@ -/*! \mainpage - * \tableofcontents - * \image html "Gudhi_banner.png" "" width=20cm - * - * \section Introduction Introduction - * The Gudhi library (Geometry Understanding in Higher Dimensions) is a generic open source C++ library for - * Computational Topology and Topological Data Analysis - * (TDA). - * 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 Algorithms to compute persistent homology and multi-field persistent homology. - * \li Simplication of simplicial complexes by edge contraction. - * - * 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" - - - - - -
- Author: Vincent Rouvreau
- Introduced in: GUDHI 1.3.0
- Copyright: GPL v3
- 		- Alpha_complex is a simplicial complex 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.
- User manual: \ref alpha_complex - Reference manual: Gudhi::alphacomplex::Alpha_complex -
- \subsection CubicalComplexDataStructure Cubical complex - \image html "Cubical_complex_representation.png" "Cubical complex representation" - - - - - -
- Author: Pawel Dlotko
- Introduced in: GUDHI 1.3.0
- Copyright: GPL v3
- 		- The cubical complex is an example of a structured complex useful in computational mathematics (specially - rigorous numerics) and image analysis.
- User manual: \ref cubical_complex - Reference manual: Gudhi::Cubical_complex::Bitmap_cubical_complex -
- \subsection SimplexTreeDataStructure Simplex tree - \image html "Simplex_tree_representation.png" "Simplex tree representation" - - - - - -
- Author: Clément Maria
- Introduced in: GUDHI 1.0.0
- Copyright: GPL v3
- 		- The simplex tree is an efficient and flexible - data structure for representing general (filtered) simplicial complexes. The data structure - is described in \cite boissonnatmariasimplextreealgorithmica .
- User manual: \ref simplex_tree - Reference manual: Gudhi::Simplex_tree -
- \subsection SkeletonBlockerDataStructure Skeleton blocker - \image html "ds_representation.png" "Skeleton blocker representation" - - - - - -
- Author: David Salinas
- Introduced in: GUDHI 1.1.0
- Copyright: GPL v3
- 		- 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.
- User manual: \ref skbl - Reference manual: Gudhi::skbl::Skeleton_blocker_complex -
- \subsection WitnessComplexDataStructure Witness complex - \image html "Witness_complex_representation.png" "Witness complex representation" - - - - - -
- Author: Siargey Kachanovich
- Introduced in: GUDHI 1.3.0
- Copyright: GPL v3
- 		- 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 .
- User manual: \ref witness_complex - Reference manual: Gudhi::witness_complex::SimplicialComplexForWitness -
- - \section Toolbox Toolbox - \subsection ContractionToolbox Contraction - \image html "sphere_contraction_representation.png" "Sphere contraction example" - - - - - -
- Author: David Salinas
- Introduced in: GUDHI 1.1.0
- Copyright: GPL v3
- 		- 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.
- User manual: \ref contr -
- \subsection PersistentCohomologyToolbox Persistent Cohomology - \image html "3DTorus_poch.png" "Rips Persistent Cohomology on a 3D Torus" - - - - - -
- Author: Clément Maria
- Introduced in: GUDHI 1.0.0
- Copyright: GPL v3
- 		- 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 .
- User manual: \ref persistent_cohomology - Reference manual: Gudhi::persistent_cohomology::Persistent_cohomology -
-*/ - -/*! \page installation Gudhi installation - * 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 demos. - * - * \section compiling Compiling - * The library uses c++11 and requires Boost with version 1.48.0 or - * more recent. It is a multi-platform library and compiles on Linux, Mac OSX and Visual Studio 2015. - * - * \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 GNU Multiple Precision Arithmetic - * Library (GMP) and will not be built if GMP is not installed: - * \li - * Persistent_cohomology/performance_rips_persistence.cpp - * \li - * Persistent_cohomology/rips_multifield_persistence.cpp - * - * Having GMP version 4.2 or higher installed is recommended. - * - * \subsection cgal CGAL: - * CGAL is a C++ library which provides easy access to efficient and reliable geometric algorithms. - * - * Having CGAL version 4.4 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 require the Computational Geometry Algorithms - * Library (CGAL \cite cgal:eb-15b) and will not be built if CGAL is not installed: - * \li - * Persistent_cohomology/alpha_complex_3d_persistence.cpp - * \li - * Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp - * \li - * Alpha_complex/Alpha_complex_from_off.cpp - * \li - * Alpha_complex/Alpha_complex_from_points.cpp - * - * The following example requires CGAL version ≥ 4.6: - * \li - * Witness_complex/witness_complex_sphere.cpp - * - * The following example requires CGAL version ≥ 4.7: - * \li - * Alpha_complex/Alpha_complex_from_off.cpp - * \li - * Alpha_complex/Alpha_complex_from_points.cpp - * \li - * Persistent_cohomology/alpha_complex_persistence.cpp - * \li - * Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp - * \li - * Persistent_cohomology/custom_persistence_sort.cpp - * - * \subsection eigen3 Eigen3: - * Eigen3 is a C++ template library for linear algebra: - * matrices, vectors, numerical solvers, and related algorithms. - * - * The following example requires the Eigen3 and will not be - * built if Eigen3 is not installed: - * \li - * Alpha_complex/Alpha_complex_from_off.cpp (requires also Eigen3) - * \li - * Alpha_complex/Alpha_complex_from_points.cpp (requires also Eigen3) - * \li - * Persistent_cohomology/alpha_complex_persistence.cpp - * \li - * Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp - * \li - * Persistent_cohomology/custom_persistence_sort.cpp - * - * \subsection tbb Threading Building Blocks: - * Intel® TBB 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 are using Intel® TBB if installed: - * \li - * Alpha_complex/Alpha_complex_from_off.cpp - * \li - * Alpha_complex/Alpha_complex_from_points.cpp - * \li - * Bitmap_cubical_complex/Bitmap_cubical_complex.cpp - * \li - * Bitmap_cubical_complex/Bitmap_cubical_complex_periodic_boundary_conditions.cpp - * \li - * Bitmap_cubical_complex/Random_bitmap_cubical_complex.cpp - * \li - * Persistent_cohomology/alpha_complex_3d_persistence.cpp - * \li - * Persistent_cohomology/alpha_complex_persistence.cpp - * \li - * Simplex_tree/simple_simplex_tree.cpp - * \li - * Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp - * \li - * Simplex_tree/simplex_tree_from_cliques_of_graph.cpp - * \li - * Persistent_cohomology/alpha_shapes_persistence.cpp - * \li - * Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp - * \li - * Persistent_cohomology/performance_rips_persistence.cpp - * \li - * Persistent_cohomology/persistence_from_file.cpp - * \li - * Persistent_cohomology/persistence_from_simple_simplex_tree.cpp - * \li - * Persistent_cohomology/plain_homology.cpp - * \li - * Persistent_cohomology/rips_multifield_persistence.cpp - * \li - * Persistent_cohomology/rips_persistence.cpp - * \li - * Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp - * \li - * Persistent_cohomology/custom_persistence_sort.cpp - * - * \subsection demos Demos and examples - * To build the demos and examples, run the following commands in a terminal: -\verbatim cd /path-to-gudhi/ -mkdir build -cd build/ -cmake .. -make \endverbatim - * A list of examples is available here. - * - * \subsection testsuites Test suites - * To test your build, run the following command in a terminal: - * \verbatim make test \endverbatim - * - * \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 -*/ - -// List of Gudhi examples - Doxygen needs at least a file tag to analyse comments -/*! @file Examples - * @example Alpha_complex/Alpha_complex_from_off.cpp - * @example Alpha_complex/Alpha_complex_from_points.cpp - * @example Bitmap_cubical_complex/Bitmap_cubical_complex.cpp - * @example Bitmap_cubical_complex/Bitmap_cubical_complex_periodic_boundary_conditions.cpp - * @example Bitmap_cubical_complex/Random_bitmap_cubical_complex.cpp - * @example common/CGAL_3D_points_off_reader.cpp - * @example common/CGAL_points_off_reader.cpp - * @example Contraction/Garland_heckbert.cpp - * @example Contraction/Rips_contraction.cpp - * @example Persistent_cohomology/alpha_complex_3d_persistence.cpp - * @example Persistent_cohomology/alpha_complex_persistence.cpp - * @example Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp - * @example Persistent_cohomology/performance_rips_persistence.cpp - * @example Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp - * @example Persistent_cohomology/persistence_from_file.cpp - * @example Persistent_cohomology/persistence_from_simple_simplex_tree.cpp - * @example Persistent_cohomology/plain_homology.cpp - * @example Persistent_cohomology/rips_multifield_persistence.cpp - * @example Persistent_cohomology/rips_persistence.cpp - * @example Persistent_cohomology/custom_persistence_sort.cpp - * @example Simplex_tree/mini_simplex_tree.cpp - * @example Simplex_tree/simple_simplex_tree.cpp - * @example Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp - * @example Simplex_tree/simplex_tree_from_cliques_of_graph.cpp - * @example Skeleton_blocker/Skeleton_blocker_from_simplices.cpp - * @example Skeleton_blocker/Skeleton_blocker_iteration.cpp - * @example Skeleton_blocker/Skeleton_blocker_link.cpp - * @example Witness_complex/witness_complex_from_file.cpp - * @example Witness_complex/witness_complex_sphere.cpp - */ - -- cgit v1.2.3