Index

A

Abstract simplicial complex annulus() (in module oat_python.point_cloud)

antitranspose_umatch_test() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) assert_almost_equal_csr() (in module oat_python.matrix) assert_symmetric_triplets_csr() (in module oat_python.matrix)

B

ball_2d() (in module oat_python.plot) barcode() (in module oat_python.plot) betti_numbers() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) blank_background() (in module oat_python.plot) boundary() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) boundary_for_chain() (oat_python.core.vietoris_rips.BoundaryMatrix method) (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method)

boundary_matrix_as_csr() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) boundary_matrix_indices_df() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) boundary_matrix_oracle() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) (oat_python.core.vietoris_rips.VietorisRipsComplex method) boundary_space_indices() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) BoundaryMatrix (class in oat_python.core.vietoris_rips) BoundaryMatrixDecomposition (class in oat_python.core.vietoris_rips) BoundaryMatrixDecompositionDowker (class in oat_python.core.dowker)

C

change_of_basis_matrix_inverse_oracle() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) change_of_basis_matrix_oracle() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) ChangeOfBasisMatrix (class in oat_python.core.vietoris_rips) ChangeOfBasisMatrixInverse (class in oat_python.core.vietoris_rips) circle() (in module oat_python.point_cloud) coboundary() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) coboundary_for_cochain() (oat_python.core.vietoris_rips.BoundaryMatrix method) (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) coboundary_space_indices() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) cocycle_indices() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) column_for_simplex() (oat_python.core.vietoris_rips.BoundaryMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrixInverse method)

column_index_for_row_index() (oat_python.core.vietoris_rips.GeneralizedMatchingMatrix method) column_indices() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) column_major() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) column_vector_dataframe_for_dense_array() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) containment_map() (in module oat_python.hypergraph) contains_3d_trace() (in module oat_python.plot) contains_a_column_for_simplex() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) contains_a_row_for_simplex() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) contains_simplex() (oat_python.core.vietoris_rips.VectorIndexTool method) contrast_initial_and_optimal_cycles_in_3d() (in module oat_python.plot) cycle_indices() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method)

D

dataframe_for_dense_array() (oat_python.core.vietoris_rips.VectorIndexTool method) dense_array_for_column_vector_dataframe() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) dense_array_for_dataframe() (oat_python.core.vietoris_rips.VectorIndexTool method) dense_array_for_row_vector_dataframe() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) diagnostic() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) Differential matrix Differential Umatch decomposition differential_comb_as_csr() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) differential_comb_inverse_as_csr() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method)

dimension() (oat_python.core.vietoris_rips.WeightedSimplex method) dimension_m_faces_as_rows_for_dimension_n_simplices_as_rows() (in module oat_python.simplex) dimension_m_faces_for_simplices() (in module oat_python.simplex) disk() (in module oat_python.point_cloud) display_dataframes_side_by_side() (in module oat_python.plot) Dissimilarity matrix Dissimilarity space dissimilarity_matrix() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) distance_iterator() (in module oat_python.dissimilarity)

E

edge_containment_graph() (in module oat_python.hypergraph) edge_containment_graph_symmetrized() (in module oat_python.hypergraph) edge_containment_relation() (in module oat_python.hypergraph) edge_containment_relation_symmetrized() (in module oat_python.hypergraph) Enclosing radius enclosing_radius_for_cloud_slow() (in module oat_python.dissimilarity) enclosing_radius_for_matrix() (in module oat_python.dissimilarity)

enclosing_radius_for_points() (in module oat_python.dissimilarity) entry_for_row_and_column() (oat_python.core.vietoris_rips.BoundaryMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrixInverse method) (oat_python.core.vietoris_rips.GeneralizedMatchingMatrix method) escolar_hiraoka_indices_df() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) euclidean_distance() (in module oat_python.dissimilarity) euclidean_distance_one_sided() (in module oat_python.dissimilarity)

F

farthest_point_sampling() (in module oat_python.dissimilarity) fig_3d_for_simplices() (in module oat_python.plot) Filter function

Filtered simple graph Filtration filtration_value() (oat_python.core.vietoris_rips.VietorisRipsComplex method) fundamental_subspace_dimensions() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method)

G

generalized_matching_matrix_as_csr() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) generalized_matching_matrix_oracle() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method)

GeneralizedMatchingMatrix (class in oat_python.core.vietoris_rips) get_matched_column() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) get_matched_row() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method)

H

half_dome() (in module oat_python.point_cloud) homology() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method)

homology_indices() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) hop_distance_for_networkx_graph() (in module oat_python.dissimilarity) hop_distance_for_simpices() (in module oat_python.dissimilarity)

I

index_number_for_simplex() (oat_python.core.vietoris_rips.VectorIndexTool method) is_column_major() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method)

is_dark_color() (in module oat_python.plot) is_structurally_zero() (in module oat_python.matrix)

L

laplacian_matrix_oracle() (oat_python.core.vietoris_rips.VietorisRipsComplex method)

LaplacianMatrix (class in oat_python.core.vietoris_rips)

M

matching_basis_vector_for_simplex() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) Matrix oracle max_finite_value() (in module oat_python.barcode) max_homology_dimension() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) mesh_rectangle() (in module oat_python.plot) minmax() (in module oat_python.matrix) module oat_python.barcode oat_python.core oat_python.core.dowker oat_python.core.vietoris_rips oat_python.dissimilarity oat_python.homology oat_python.hypergraph oat_python.matrix oat_python.plot oat_python.point_cloud oat_python.simplex

N

networkx_graph_for_simplices() (in module oat_python.simplex) networkx_nerve_for_hypergraph() (in module oat_python.hypergraph) nonzero_entries() (oat_python.core.vietoris_rips.GeneralizedMatchingMatrix method)

number_of_columns() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) number_of_rows() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) number_of_simplices() (oat_python.core.vietoris_rips.VectorIndexTool method)

O

oat_python.barcode module oat_python.core module oat_python.core.dowker module oat_python.core.vietoris_rips module oat_python.dissimilarity module oat_python.homology module oat_python.hypergraph module

oat_python.matrix module oat_python.plot module oat_python.point_cloud module oat_python.simplex module optimize_bounding_chain() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) optimize_bounding_chain_kernel() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) optimize_cycle() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method)

P

persistence_diagram() (in module oat_python.plot) persistence_diagram_guidelines() (in module oat_python.plot) persistent_homology_dataframe() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) product_with_column_vector() (oat_python.core.vietoris_rips.ChangeOfBasisMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrixInverse method)

product_with_row_vector() (oat_python.core.vietoris_rips.ChangeOfBasisMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrixInverse method) product_with_vector() (oat_python.core.vietoris_rips.LaplacianMatrix method)

R

reduce_hypergraph() (in module oat_python.hypergraph) reduce_hypergraph_with_labels() (in module oat_python.hypergraph) relabel() (in module oat_python.hypergraph) row_for_simplex() (oat_python.core.vietoris_rips.BoundaryMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrixInverse method) (oat_python.core.vietoris_rips.LaplacianMatrix method)

row_index_for_column_index() (oat_python.core.vietoris_rips.GeneralizedMatchingMatrix method) row_indices() (oat_python.core.dowker.BoundaryMatrixDecompositionDowker method) (oat_python.core.vietoris_rips.SubmatrixIndexTool method) row_vector_dataframe_for_dense_array() (oat_python.core.vietoris_rips.SubmatrixIndexTool method)

S

Scipy sparse CSR matrices set_background_color() (in module oat_python.plot) set_column_indices() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) set_row_indices() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) set_simplices() (oat_python.core.vietoris_rips.VectorIndexTool method) Simple graph simplex() (oat_python.core.vietoris_rips.WeightedSimplex method) simplex_for_index_number() (oat_python.core.vietoris_rips.VectorIndexTool method) simplices() (oat_python.core.vietoris_rips.VectorIndexTool method) simplices_for_dimensions() (oat_python.core.vietoris_rips.VietorisRipsComplex method) solve_dx_equals_b() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) solve_xd_equals_b() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) Sparse dissimilarity matrix Sparse matrix sparse_dataframe_for_csr_matrix() (oat_python.core.vietoris_rips.SubmatrixIndexTool method)

sparse_matrix_for_cloud_slow() (in module oat_python.dissimilarity) sparse_matrix_for_csr() (in module oat_python.dissimilarity) sparse_matrix_for_dense() (in module oat_python.dissimilarity) sparse_matrix_for_points() (in module oat_python.dissimilarity) sphere_or_slice() (in module oat_python.point_cloud) sphere_or_slice_spiral() (in module oat_python.point_cloud) stanford_dragon() (in module oat_python.point_cloud) submatrix_column_number_for_simplex() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) submatrix_index_tool() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) (oat_python.core.vietoris_rips.VietorisRipsComplex method) submatrix_row_number_for_simplex() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) SubmatrixIndexTool (class in oat_python.core.vietoris_rips) surface_cube() (in module oat_python.plot) surface_octahedron() (in module oat_python.plot) surface_rectangle() (in module oat_python.plot) surface_sphere() (in module oat_python.plot)

T

test_dissimilarity_matrix() (in module oat_python.dissimilarity) test_minmax() (in module oat_python.matrix) test_validate_dissimilarity_matrix() (in module oat_python.dissimilarity) test_validate_square_and_symmetric_matrix() (in module oat_python.matrix) torus() (in module oat_python.point_cloud) torus_curve() (in module oat_python.point_cloud) trace_2d_for_edge() (in module oat_python.plot) trace_2d_for_edges() (in module oat_python.plot) trace_2d_for_triangle() (in module oat_python.plot)

trace_2d_for_triangles() (in module oat_python.plot) trace_2d_for_vertices() (in module oat_python.plot) trace_3d_for_edge() (in module oat_python.plot) trace_3d_for_edges() (in module oat_python.plot) trace_3d_for_triangles() (in module oat_python.plot) trace_3d_for_vertices() (in module oat_python.plot) transpose() (in module oat_python.hypergraph) transpose_listlist() (in module oat_python.core.dowker) triplets_for_csr() (in module oat_python.matrix) two_circles() (in module oat_python.point_cloud)

U

Umatch decomposition unique_elements() (in module oat_python.hypergraph)

unique_row_indices() (in module oat_python.core.dowker) unique_rows() (in module oat_python.core.dowker) unique_values() (in module oat_python.hypergraph)

V

validate_dissimilarity_matrix() (in module oat_python.dissimilarity) validate_simplex_dimension() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrixInverse method) (oat_python.core.vietoris_rips.GeneralizedMatchingMatrix method) validate_square_and_symmetric_matrix() (in module oat_python.matrix) vector_index_tool() (oat_python.core.vietoris_rips.VietorisRipsComplex method)

VectorIndexTool (class in oat_python.core.vietoris_rips) vertex_embedding_for_networkx_graph() (in module oat_python.plot) vertex_embedding_for_simplices() (in module oat_python.plot) vertices_incident_to_simplices() (in module oat_python.simplex) Vietoris Rips complex vietoris_rips_complex() (oat_python.core.vietoris_rips.BoundaryMatrixDecomposition method) VietorisRipsComplex (class in oat_python.core.vietoris_rips)

W

weight() (oat_python.core.vietoris_rips.WeightedSimplex method) weighted_simplex_for_submatrix_column_number() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) weighted_simplex_for_submatrix_row_number() (oat_python.core.vietoris_rips.SubmatrixIndexTool method) WeightedSimplex (class in oat_python.core.vietoris_rips) wire_rectangle() (in module oat_python.plot)

wire_sphere_3d() (in module oat_python.plot) write_submatrix_to_csr() (oat_python.core.vietoris_rips.BoundaryMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrix method) (oat_python.core.vietoris_rips.ChangeOfBasisMatrixInverse method) (oat_python.core.vietoris_rips.GeneralizedMatchingMatrix method) write_to_dataframe() (oat_python.core.vietoris_rips.GeneralizedMatchingMatrix method)

Z

zigzag_homology() (in module oat_python.core.dowker)