diff options
Diffstat (limited to 'src/Persistent_cohomology/doc/Intro_persistent_cohomology.h')
| -rw-r--r-- | src/Persistent_cohomology/doc/Intro_persistent_cohomology.h | 69 |
1 files changed, 36 insertions, 33 deletions
diff --git a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h index a16591ce..6fd19706 100644 --- a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h +++ b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h @@ -144,6 +144,8 @@ diagram. 3 1 0.104347 inf 3 2 0.138335 inf \endcode +More details on the <a href="../../ripscomplex/">Rips complex utilities</a> dedicated page. + \li <a href="_persistent_cohomology_2rips_multifield_persistence_8cpp-example.html"> Persistent_cohomology/rips_multifield_persistence.cpp</a> computes the Rips complex of a point cloud and outputs its persistence diagram with a family of field coefficients. @@ -156,6 +158,8 @@ The file should contain square or lower triangular distance matrix with semicolo The code do not check if it is dealing with a distance matrix. It is the user responsibility to provide a valid input. Please refer to data/distance_matrix/lower_triangular_distance_matrix.csv for an example of a file. +More details on the <a href="../../ripscomplex/">Rips complex utilities</a> dedicated page. + \li <a href="_rips_complex_2rips_correlation_matrix_persistence_8cpp-example.html"> Rips_complex/rips_correlation_matrix_persistence.cpp</a> computes the Rips complex of a correlation matrix and outputs its persistence diagram. @@ -165,6 +169,8 @@ It is the user responsibility to ensure that this is the case. The input is to b triangular matrix. Please refer to data/correlation_matrix/lower_triangular_correlation_matrix.csv for an example of a file. +More details on the <a href="../../ripscomplex/">Rips complex utilities</a> dedicated page. + \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. @@ -175,48 +181,33 @@ Alpha_complex/alpha_complex_3d_persistence.cpp</a> computes the persistent homol 2 1 0.0934117 1.00003 2 2 0.56444 1.03938 \endcode -\li <a href="_alpha_complex_2exact_alpha_complex_3d_persistence_8cpp-example.html"> -Alpha_complex/exact_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with -\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. -Here, as CGAL computes the exact values, it is slower, but it is necessary when points are on a grid -for instance. -\code $> ./exact_alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off -p 2 -m 0.1 \endcode +More details on the <a href="../../alphacomplex/">Alpha complex utilities</a> dedicated page. + +CGAL can be forced to compute the exact values, it is slower, but it is necessary when points are on a grid +for instance (the fast version `--fast` would give incorrect values). +\code $> ./alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off --exact -p 2 -m 0.1 \endcode \code Simplex_tree dim: 3 2 0 0 inf 2 2 0.0002 0.2028 \endcode -\li <a href="_alpha_complex_2weighted_alpha_complex_3d_persistence_8cpp-example.html"> -Alpha_complex/weighted_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +It can also compute the persistent homology with \f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the weighted alpha complex on points sampling from an OFF file and a weights file. -\code $> ./weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off -../../data/points/tore3D_300.weights -p 2 -m 0.45 \endcode +\code $> ./alpha_complex_3d_persistence ../../data/points/tore3D_300.off +--weight-file ../../data/points/tore3D_300.weights -p 2 -m 0.45 \endcode \code Simplex_tree dim: 3 2 0 -1 inf 2 1 -0.931784 0.000103311 2 1 -0.906588 2.60165e-05 2 2 -0.43556 0.0393798 \endcode -\li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html"> -Alpha_complex/alpha_complex_persistence.cpp</a> computes the persistent homology with -\f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. -\code $> ./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off \endcode -\code Alpha complex is of dimension 3 - 9273 simplices - 300 vertices. -Simplex_tree dim: 3 -2 0 0 inf -2 1 0.0682162 1.0001 -2 1 0.0934117 1.00003 -2 2 0.56444 1.03938 \endcode - -\li <a href="_alpha_complex_2periodic_alpha_complex_3d_persistence_8cpp-example.html"> -Alpha_complex/periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +One can also compute the persistent homology with \f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the periodic alpha complex on points sampling from an OFF file. The second parameter is a \ref FileFormatsIsoCuboid file with coordinates of the periodic cuboid. Note that the lengths of the sides of the periodic cuboid have to be the same. -\code $> ./periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off -../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0 \endcode -\code Periodic Delaunay computed. -Simplex_tree dim: 3 +\code $> ./alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off +--cuboid-file ../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0 \endcode +\code Simplex_tree dim: 3 3 0 0 inf 3 1 0.0025 inf 3 1 0.0025 inf @@ -226,18 +217,17 @@ Simplex_tree dim: 3 3 2 0.005 inf 3 3 0.0075 inf \endcode -\li <a href="_persistent_cohomology_2weighted_periodic_alpha_complex_3d_persistence_8cpp-example.html"> -Persistent_cohomology/weighted_periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +In order to compute the persistent homology with \f$\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 +\code $> ./alpha_complex_3d_persistence ../../data/points/shifted_sphere.off +--weight-file ../../data/points/shifted_sphere.weights +--cuboid-file ../../data/points/iso_cuboid_3_in_0_10.txt -p 3 -m 1.0 \endcode +\code Simplex_tree dim: 3 3 0 -0.0001 inf 3 1 16.0264 inf 3 1 16.0273 inf @@ -247,6 +237,19 @@ Simplex_tree dim: 3 3 2 36.8838 inf 3 3 58.6783 inf \endcode +\li <a href="_alpha_complex_2alpha_complex_persistence_8cpp-example.html"> +Alpha_complex/alpha_complex_persistence.cpp</a> computes the persistent homology with +\f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. +\code $> ./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off \endcode +\code Alpha complex is of dimension 3 - 9273 simplices - 300 vertices. +Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 \endcode + +More details on the <a href="../../alphacomplex/">Alpha complex utilities</a> dedicated page. + \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. |