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Diffstat (limited to 'doc/Persistent_cohomology/Intro_persistent_cohomology.h')
| -rw-r--r-- | doc/Persistent_cohomology/Intro_persistent_cohomology.h | 60 |
1 files changed, 41 insertions, 19 deletions
diff --git a/doc/Persistent_cohomology/Intro_persistent_cohomology.h b/doc/Persistent_cohomology/Intro_persistent_cohomology.h index 6400116b..4dbe82c7 100644 --- a/doc/Persistent_cohomology/Intro_persistent_cohomology.h +++ b/doc/Persistent_cohomology/Intro_persistent_cohomology.h @@ -143,8 +143,8 @@ namespace persistent_cohomology { 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 outputs its persistence +\li <a href="_rips_complex_2rips_persistence_8cpp-example.html"> +Rips_complex/rips_persistence.cpp</a> computes the Rips complex of a point cloud and outputs its persistence diagram. \code $> ./rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3 \endcode \code The complex contains 177838 simplices @@ -158,44 +158,44 @@ diagram. Persistent_cohomology/rips_multifield_persistence.cpp</a> computes the Rips complex of a point cloud and outputs its persistence diagram with a family of field coefficients. -\li <a href="_persistent_cohomology_2rips_distance_matrix_persistence_8cpp-example.html"> -Persistent_cohomology/rips_distance_matrix_persistence.cpp</a> computes the Rips complex of a distance matrix and +\li <a href="_rips_complex_2rips_distance_matrix_persistence_8cpp-example.html"> +Rips_complex/rips_distance_matrix_persistence.cpp</a> computes the Rips complex of a distance matrix and outputs its persistence diagram. -\li <a href="_persistent_cohomology_2alpha_complex_3d_persistence_8cpp-example.html"> -Persistent_cohomology/alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\li <a href="_alpha_complex_2alpha_complex_3d_persistence_8cpp-example.html"> +Alpha_complex/alpha_complex_3d_persistence.cpp</a> computes the persistent homology with \f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. -\code $> ./alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45 \endcode +\code $> ./alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45 \endcode \code Simplex_tree dim: 3 2 0 0 inf 2 1 0.0682162 1.0001 2 1 0.0934117 1.00003 2 2 0.56444 1.03938 \endcode -\li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html"> -Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\li <a href="_alpha_complex_2exact_alpha_complex_3d_persistence_8cpp-example.html"> +Alpha_complex/exact_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with \f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. Here, as CGAL computes the exact values, it is slower, but it is necessary when points are on a grid for instance. -\code $> ./exact_alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off 2 0.1 \endcode +\code $> ./exact_alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off -p 2 -m 0.1 \endcode \code Simplex_tree dim: 3 2 0 0 inf 2 2 0.0002 0.2028 \endcode -\li <a href="_persistent_cohomology_2weighted_alpha_complex_3d_persistence_8cpp-example.html"> -Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\li <a href="_alpha_complex_2weighted_alpha_complex_3d_persistence_8cpp-example.html"> +Alpha_complex/weighted_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with \f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the weighted alpha complex on points sampling from an OFF file and a weights file. \code $> ./weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off -../../data/points/tore3D_300.weights 2 0.45 \endcode +../../data/points/tore3D_300.weights -p 2 -m 0.45 \endcode \code Simplex_tree dim: 3 2 0 -1 inf 2 1 -0.931784 0.000103311 2 1 -0.906588 2.60165e-05 2 2 -0.43556 0.0393798 \endcode -\li <a href="_persistent_cohomology_2alpha_complex_persistence_8cpp-example.html"> -Persistent_cohomology/alpha_complex_persistence.cpp</a> computes the persistent homology with +\li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html"> +Alpha_complex/alpha_complex_persistence.cpp</a> computes the persistent homology with \f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. \code $> ./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off \endcode \code Alpha complex is of dimension 3 - 9273 simplices - 300 vertices. @@ -205,11 +205,13 @@ Simplex_tree dim: 3 2 1 0.0934117 1.00003 2 2 0.56444 1.03938 \endcode -\li <a href="_persistent_cohomology_2periodic_alpha_complex_3d_persistence_8cpp-example.html"> -Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html"> +Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with \f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the periodic alpha complex on points sampling from an OFF file. +The second parameter is a \ref FileFormatsIsoCuboid file with coordinates of the periodic cuboid. +Note that the lengths of the sides of the periodic cuboid have to be the same. \code $> ./periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off -../../data/points/iso_cuboid_3_in_0_1.txt 3 1.0 \endcode +../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0 \endcode \code Periodic Delaunay computed. Simplex_tree dim: 3 3 0 0 inf @@ -221,11 +223,31 @@ Simplex_tree dim: 3 3 2 0.005 inf 3 3 0.0075 inf \endcode +\li <a href="_persistent_cohomology_2weighted_periodic_alpha_complex_3d_persistence_8cpp-example.html"> +Persistent_cohomology/weighted_periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the periodic alpha complex on weighted points from an OFF file. The +additional parameters of this program are:<br> +(a) The file with the weights of points. The file consist of a sequence of numbers (as many as points). +Note that the weight of each single point have to be bounded by 1/64 times the square of the cuboid edge length.<br> +(b) A \ref FileFormatsIsoCuboid file with coordinates of the periodic cuboid. +Note that the lengths of the sides of the periodic cuboid have to be the same.<br> +\code $> ./weighted_periodic_alpha_complex_3d_persistence ../../data/points/shifted_sphere.off +../../data/points/shifted_sphere.weights ../../data/points/iso_cuboid_3_in_0_10.txt 3 1.0 \endcode +\code Weighted Periodic Delaunay computed. +Simplex_tree dim: 3 +3 0 -0.0001 inf +3 1 16.0264 inf +3 1 16.0273 inf +3 1 16.0303 inf +3 2 36.8635 inf +3 2 36.8704 inf +3 2 36.8838 inf +3 3 58.6783 inf \endcode + \li <a href="_persistent_cohomology_2plain_homology_8cpp-example.html"> Persistent_cohomology/plain_homology.cpp</a> computes the plain homology of a simple simplicial complex without filtration values. - \copyright GNU General Public License v3. */ } // namespace persistent_cohomology |