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Diffstat (limited to 'doc/Persistent_cohomology/Intro_persistent_cohomology.h')
| -rw-r--r-- | doc/Persistent_cohomology/Intro_persistent_cohomology.h | 44 |
1 files changed, 36 insertions, 8 deletions
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 <a href="_persistent_cohomology_2rips_persistence_8cpp-example.html"> -Persistent_cohomology/rips_persistence.cpp</a> computes the Rips complex of a point cloud and its persistence diagram. +Persistent_cohomology/rips_persistence.cpp</a> computes the Rips complex of a point cloud and outputs its persistence +diagram. +\code $> ./rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3 \endcode +\code The complex contains 177838 simplices + and has dimension 3 +3 0 0 inf +3 1 0.0983494 inf +3 1 0.104347 inf +3 2 0.138335 inf \endcode \li <a href="_persistent_cohomology_2rips_multifield_persistence_8cpp-example.html"> -Persistent_cohomology/rips_multifield_persistence.cpp</a> computes the Rips complex of a point cloud and its +Persistent_cohomology/rips_multifield_persistence.cpp</a> computes the Rips complex of a point cloud and outputs its persistence diagram with a family of field coefficients. -\li <a href="_persistent_cohomology_2performance_rips_persistence_8cpp-example.html"> -Persistent_cohomology/performance_rips_persistence.cpp</a> provides timings for the construction of the Rips complex -on a set of points sampling a Klein bottle in \f$\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 <a href="_persistent_cohomology_2rips_distance_matrix_persistence_8cpp-example.html"> +Persistent_cohomology/rips_distance_matrix_persistence.cpp</a> computes the Rips complex of a distance matrix and +outputs its persistence diagram. \li <a href="_persistent_cohomology_2alpha_complex_3d_persistence_8cpp-example.html"> Persistent_cohomology/alpha_complex_3d_persistence.cpp</a> computes the persistent homology with @@ -166,6 +172,28 @@ Persistent_cohomology/alpha_complex_3d_persistence.cpp</a> computes the persiste 2 1 0.0934117 1.00003 2 2 0.56444 1.03938 \endcode +\li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html"> +Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. +Here, as CGAL computes the exact values, it is slower, but it is necessary when points are on a grid +for instance. +\code $> ./exact_alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off 2 0.1 \endcode +\code Simplex_tree dim: 3 +2 0 0 inf +2 2 0.0002 0.2028 \endcode + +\li <a href="_persistent_cohomology_2weighted_alpha_complex_3d_persistence_8cpp-example.html"> +Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the weighted alpha complex on points sampling from an OFF file +and a weights file. +\code $> ./weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off +../../data/points/tore3D_300.weights 2 0.45 \endcode +\code Simplex_tree dim: 3 +2 -0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 \endcode + \li <a href="_persistent_cohomology_2alpha_complex_persistence_8cpp-example.html"> Persistent_cohomology/alpha_complex_persistence.cpp</a> computes the persistent homology with \f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. |