{ "_id": "6abd1ed199f7aa8c6aa4f69b", "Package": "SimplicialComplex", "Type": "Package", "Title": "Topological Data Analysis: Simplicial Complex", "Version": "0.2.1", "Authors@R": "c(person(\"ChiChien\", \"Wang\", email = \"kennywang2003@gmail.com\", role = c(\"aut\", \"cre\", \"trl\")))", "Maintainer": "ChiChien Wang ", "Description": "Provides an implementation of simplicial complexes for\nTopological Data Analysis (TDA). The package includes functions\nto compute faces, boundary operators, Betti numbers, Euler\ncharacteristic, and to construct simplicial complexes,\nincluding Vietoris-Rips, Cech, Alpha, Delaunay, Witness, flood,\nand (via a Freudenthal triangulation) cubical complexes for\ngrid and image data. It also implements persistent homology,\nfrom building filtrations (via a single build_filtration()\nentry point covering all of the above) to computing persistence\ndiagrams, persistence landscapes, and Wasserstein/bottleneck\ndistances between diagrams, with the aim of helping readers\nunderstand the core concepts of computational topology. Methods\nare based on standard references in persistent homology such as\nZomorodian and Carlsson (2005) ,\nChazal and Michel (2021) , and\nOtter, Porter, Tillmann, Grindrod and Harrington (2017)\n.", "License": "MIT + file LICENSE", "URL": "https://github.com/TDA-R/SimplicialComplex", "BugReports": "https://github.com/TDA-R/SimplicialComplex/issues", "Encoding": "UTF-8", "RoxygenNote": "7.3.2", "Config/testthat/edition": "3", "Config/pak/sysreqs": "libglpk-dev libxml2-dev", "Repository": "https://tda-r.r-universe.dev", "Date/Publication": "2026-09-30 12:09:33 UTC", "RemoteUrl": "https://github.com/tda-r/simplicialcomplex", "RemoteRef": "HEAD", "RemoteSha": "c39c7ad4497fe98c1fc3530ecd25d43ddb4c486c", "NeedsCompilation": "no", "Packaged": { "Date": "2026-09-30 14:26:58 UTC", "User": "root" }, "Author": "ChiChien Wang [aut, cre, trl]", "_user": "tda-r", "_type": "src", "_file": "SimplicialComplex_0.2.1.tar.gz", "_fileid": 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}, { "page": "bottleneck_distance", "title": "Bottleneck distance between two persistence diagrams", "topics": [ "bottleneck_distance" ] }, { "page": "boundary", "title": "Compute the boundary operator for a simplicial complex", "topics": [ "boundary" ] }, { "page": "boundary_info", "title": "Get the boundary matrix and its reduction information in matrix form", "topics": [ "boundary_info" ] }, { "page": "build_cubical_filtration", "title": "Build a cubical (grid) filtration from an image", "topics": [ "build_cubical_filtration" ] }, { "page": "build_filtration", "title": "Build a filtration from a point cloud, for any of five complex types", "topics": [ "build_filtration" ] }, { "page": "build_flood_filtration", "title": "Flood filtration in SimplicialComplex format", "topics": [ "build_flood_filtration" ] }, { "page": "CechComplex", "title": "Construct a Cech Complex", "topics": [ "CechComplex" ] }, { "page": "collect_g", "title": "Collect 1-unstable manifolds into a reconstructed graph", "topics": [ "collect_g" ] }, { "page": "compare_complexes", "title": "Compare simplicial complex constructions on one point cloud", "topics": [ "compare_complexes" ] }, { "page": "complex_distance", "title": "Wasserstein/bottleneck distance between two point clouds, via one chosen complex", "topics": [ "complex_distance" ] }, { "page": "crocker", "title": "Compute a CROCKER matrix for a time-varying point cloud", "topics": [ "crocker" ] }, { "page": "DelaunayComplex", "title": "Construct a Delaunay Complex", "topics": [ "DelaunayComplex" ] }, { "page": "diagram_matching", "title": "Optimal point matching between two persistence diagrams", "topics": [ "diagram_matching" ] }, { "page": "euler_characteristic", "title": "Compute the Euler characteristic chi of a simplicial complex", "topics": [ "euler_characteristic" ] }, { "page": "extract_persistence_pairs", "title": "This function extracts the persistence from combining the boundary matrix and its filtration", "topics": [ "extract_persistence_pairs" ] }, { "page": "faces", "title": "Generate all unique faces of a given dimension from simplices", "topics": [ "faces" ] }, { "page": "flood_complex", "title": "Construct a Flood complex", "topics": [ "flood_complex" ] }, { "page": "flood_persistence", "title": "Persistence pairs via sparse boundary reduction", "topics": [ "flood_persistence" ] }, { "page": "gauss_jordan_eliminate", "title": "Row-reduce (partial pivoting) a matrix", "topics": [ "gauss_jordan_eliminate" ] }, { "page": "generate_landmarks", "title": "Farthest-Point Sampling of landmarks", "topics": [ "generate_landmarks" ] }, { "page": "graph_laplacian", "title": "Basic graph Laplacian L = D - A", "topics": [ "graph_laplacian" ] }, { "page": "hodge_laplacian", "title": "Ordinary Hodge Laplacian", "topics": [ "hodge_laplacian" ] }, { "page": "homology", "title": "Compute a homology basis from a cycle basis and a boundary basis", "topics": [ "homology" ] }, { "page": "im", "title": "Compute a 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filtrations)", "topics": [ "persistence_pairs" ] }, { "page": "persistent_laplacian", "title": "Persistent (combinatorial) Laplacian", "topics": [ "persistent_laplacian" ] }, { "page": "plot_crocker", "title": "Plot a CROCKER matrix as a filled contour plot", "topics": [ "plot_crocker" ] }, { "page": "plot_landscape", "title": "Plot a Persistence Landscape", "topics": [ "plot_landscape" ] }, { "page": "plot_matching", "title": "Plot the optimal matching between two persistence diagrams", "topics": [ "plot_matching" ] }, { "page": "plot_morse_landscape", "title": "Plot the density landscape and critical structure in interactive 3D", "topics": [ "plot_morse_landscape" ] }, { "page": "plot_morse_recon", "title": "Plot the graph reconstructed by 'morse_recon'", "topics": [ "plot_morse_recon" ] }, { "page": "plot_morse_vpath", "title": "Plot a local patch of the triangulation with its discrete gradient field", "topics": [ "plot_morse_vpath" ] }, { "page": "plot_persistence", "title": "Plot 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