Topological Data Analysis: Simplicial Complex

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Documentation for package ‘SimplicialComplex’ version 0.2.1

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AlphaComplex Construct an Alpha Complex
as_filtration Convert a flood_complex object to a filtration list
bottleneck_distance Bottleneck distance between two persistence diagrams
boundary Compute the boundary operator for a simplicial complex
boundary_info Get the boundary matrix and its reduction information in matrix form
build_cubical_filtration Build a cubical (grid) filtration from an image
build_filtration Build a filtration from a point cloud, for any of five complex types
build_flood_filtration Flood filtration in SimplicialComplex format
CechComplex Construct a Cech Complex
collect_g Collect 1-unstable manifolds into a reconstructed graph
compare_complexes Compare simplicial complex constructions on one point cloud
complex_distance Wasserstein/bottleneck distance between two point clouds, via one chosen complex
crocker Compute a CROCKER matrix for a time-varying point cloud
DelaunayComplex Construct a Delaunay Complex
diagram_matching Optimal point matching between two persistence diagrams
euler_characteristic Compute the Euler characteristic chi of a simplicial complex
extract_persistence_pairs This function extracts the persistence from combining the boundary matrix and its filtration
faces Generate all unique faces of a given dimension from simplices
flood_complex Construct a Flood complex
flood_persistence Persistence pairs via sparse boundary reduction
gauss_jordan_eliminate Row-reduce (partial pivoting) a matrix
generate_landmarks Farthest-Point Sampling of landmarks
graph_laplacian Basic graph Laplacian L = D - A
hodge_laplacian Ordinary Hodge Laplacian
homology Compute a homology basis from a cycle basis and a boundary basis
im Compute a basis for the image (column space) of a matrix
ker Compute a basis for the kernel (null space) of a matrix
lower_star_filtration Generalizes 'build_cubical_filtration' to any triangulation: given the maximal simplices of a simplicial complex and a function defined at its vertices, builds the simplex-wise lower-star filtration \mathcal{F}_f.
morse_recon Reconstruct a hidden graph from a density field
partial_pers_dmvf Persistence-guided discrete Morse vector field on a graph (1-complex)
persistence_landscape Compute the persistence landscape of a persistence diagram
persistence_pairs Persistence pairs via sparse boundary reduction (for large filtrations)
persistent_laplacian Persistent (combinatorial) Laplacian
plot_crocker Plot a CROCKER matrix as a filled contour plot
plot_landscape Plot a Persistence Landscape
plot_matching Plot the optimal matching between two persistence diagrams
plot_morse_landscape Plot the density landscape and critical structure in interactive 3D
plot_morse_recon Plot the graph reconstructed by 'morse_recon'
plot_morse_vpath Plot a local patch of the triangulation with its discrete gradient field
plot_persistence Plot Persistence Diagram
restrict_filtration Restrict a filtration list to simplices up to a given dimension
VietorisRipsComplex Construct a Vietoris–Rips Complex (1-skeleton + maximal simplices)
wasserstein_distance Wasserstein distance between two persistence diagrams
WitnessComplex Construct a Witness Complex
zigzag_persistence Compute the persistence barcode of a zigzag filtration of simplicial complexes