FiltrationValue Struct Reference

Value type for a filtration function on a cell complex. More...

#include <concept/Simplex_tree/FiltrationValue.h>

Public Member Functions

bool operator< (FiltrationValue f1, FiltrationValue f2)
 Operator < is a StrictWeakOrdering.
 

Detailed Description

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_3d_persistence.cpp, alpha_complex_persistence.cpp, alpha_rips_persistence_bottleneck_distance.cpp, cech_complex_cgal_mini_sphere_3d.cpp, cech_complex_example_from_points.cpp, cech_persistence.cpp, distance_matrix_edge_collapse_rips_persistence.cpp, edge_collapse_basic_example.cpp, edge_collapse_conserve_persistence.cpp, example_one_skeleton_rips_from_correlation_matrix.cpp, example_one_skeleton_rips_from_distance_matrix.cpp, example_one_skeleton_rips_from_points.cpp, example_rips_complex_from_csv_distance_matrix_file.cpp, example_rips_complex_from_off_file.cpp, example_sparse_rips.cpp, persistence_from_file.cpp, persistence_from_simple_simplex_tree.cpp, point_cloud_edge_collapse_rips_persistence.cpp, rips_correlation_matrix_persistence.cpp, rips_distance_matrix_persistence.cpp, rips_multifield_persistence.cpp, rips_persistence.cpp, rips_persistence_step_by_step.cpp, rips_persistence_via_boundary_matrix.cpp, simple_simplex_tree.cpp, simplex_tree_from_cliques_of_graph.cpp, sparse_rips_persistence.cpp, strong_witness_persistence.cpp, and weak_witness_persistence.cpp.

The documentation for this struct was generated from the following file: