Value type for a filtration function on a cell complex.
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Value type for a filtration function on a cell complex.
A filtration of a cell complex (see FilteredComplex) is a function f:\mathbf{K} \rightarrow \mathbb{R} satisfying f(\tau)\leq f(\sigma) whenever \tau \subseteq \sigma. Ordering the simplices by increasing filtration values (breaking ties so as a simplex appears after its subsimplices of same filtration value) provides an indexing scheme (see IndexingTag).
- Examples:
- Alpha_complex/alpha_complex_3d_persistence.cpp, Alpha_complex/alpha_complex_persistence.cpp, Alpha_complex/exact_alpha_complex_3d_persistence.cpp, Alpha_complex/periodic_alpha_complex_3d_persistence.cpp, Alpha_complex/weighted_alpha_complex_3d_persistence.cpp, Alpha_complex/weighted_periodic_alpha_complex_3d_persistence.cpp, Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp, Persistent_cohomology/persistence_from_file.cpp, Persistent_cohomology/persistence_from_simple_simplex_tree.cpp, Persistent_cohomology/rips_multifield_persistence.cpp, Persistent_cohomology/rips_persistence_step_by_step.cpp, Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp, Rips_complex/example_one_skeleton_rips_from_distance_matrix.cpp, Rips_complex/example_one_skeleton_rips_from_points.cpp, Rips_complex/example_rips_complex_from_csv_distance_matrix_file.cpp, Rips_complex/example_rips_complex_from_off_file.cpp, Rips_complex/rips_distance_matrix_persistence.cpp, Rips_complex/rips_persistence.cpp, Simplex_tree/cech_complex_cgal_mini_sphere_3d.cpp, Simplex_tree/simple_simplex_tree.cpp, Simplex_tree/simplex_tree_from_cliques_of_graph.cpp, Witness_complex/strong_witness_persistence.cpp, and Witness_complex/weak_witness_persistence.cpp.
The documentation for this struct was generated from the following file:
