Namespace bats

Detailed Description

We need to specify what is the conventional usage of permutation in bats!! [2, 0, 1] apply to [2.0 , 1.0 ,5.0] a) is [5.0, 2.0, 1.0] in matrix permutation notation b) is [1.0, 5.0 ,2.0] in traditioanl notation(in book From Mathematics to Generic Programming) We take the frist notation here, but notice that BATs, sometimes, will mix the two notations!!! Check before use!!! Since the above two notations are inverse to each other, inverse them if needed! Constructions on a grid Freudenthal triangulation

Namespaces

• Namespace bats::detail

• Namespace bats::flags

• Namespace bats::future

• Namespace bats::rowmajor

• Namespace bats::util

• Namespace bats::zigzag

Classes

• Template Struct AbstractMetric

• Struct AngleDist

• Struct apparent_pairs_flag

• Struct bar

• Template Struct ChainComplex

• Template Struct ChainMap

• Struct clearing_flag

• Template Struct CochainComplex

• Struct compression_flag

• Struct compute_basis_flag

• Struct CosineDist

• Template Struct DataSet

• Template Struct DGLinearMap

• Template Struct DGVectorSpace

• Struct Diagram::Edge

• Struct divide_conquer_flag

• Struct Euclidean

• Struct extra_reduction_flag

• Template Struct filtered_edge

• Template Struct FilteredChainComplex

• Template Struct FilteredCochainComplex

• Template Struct FilteredDGVectorSpace

• Struct L1Dist

• Struct LightSimplicialComplex::simplex_boundary_iterator

• Struct LInfDist

• Struct no_apparent_pairs_flag

• Struct no_optimization_flag

• Template Struct PersistencePair

• Template Struct ReducedDGVectorSpace

• Template Struct ReducedFilteredChainComplex

• Template Struct ReducedFilteredDGVectorSpace

• Struct RPAngleDist

• Struct RPCosineDist

• Struct sparse_reduction_flag

• Struct standard_reduction_flag

• Template Struct tedge

• Struct triangle

• Template Struct Update_info

• Struct UpdateInfo2

• Template Class BarcodePair

• Class CellComplex

• Class CellularMap

• Class CubicalComplex

• Template Class Diagram

• Template Class Filtration

• Template Class LightSimplicialComplex

• Template Class ReducedChainComplex

• Template Class ReducedCochainComplex

• Class SimplicialComplex

• Template Class SparseTrie

Functions

• Template Function bats::__ChainComplex(const CpxT&, T)

• Template Function bats::__ChainComplex(const CpxT&, const CpxT&, T)

• Template Function bats::__ChainFunctor

• Template Function bats::__CochainComplex

• Template Function bats::__FilteredChainComplex

• Template Function bats::__ReducedChainComplex

• Template Function bats::__ReducedCochainComplex

• Template Function bats::__ReducedFilteredChainComplex

• Template Function bats::add_dimension_recursive_flag(CpxT&, const NT&, const size_t, const size_t, const std::vector<size_t>&, std::vector<size_t>&)

• Template Function bats::add_dimension_recursive_flag(Filtration<T, CpxT>&, const NT&, const size_t, const size_t, const std::vector<size_t>&, std::vector<size_t>&, const T&)

• Template Function bats::add_dimension_recursive_flag(Filtration<T, CpxT>&, const NT&, const size_t, const size_t, const std::vector<size_t>&, std::vector<size_t>&, const T&, bool, const cell_ind&)

• Template Function bats::add_dimension_recursive_flag_extension

• Template Function bats::add_dimension_recursive_flag_unsafe

• Function bats::add_dimension_recursive_nerve

• Template Function bats::add_normal_noise(Matrix<T>&, const T, const T)

• Template Function bats::add_normal_noise(Matrix<T>&, unsigned, const T, const T)

• Template Function bats::add_normal_noise(DataSet<T>&, const T, const T)

• Template Function bats::add_normal_noise(DataSet<T>&, unsigned, const T, const T)

• Template Function bats::add_uniform_noise(Matrix<T>&, unsigned, const T, const T)

• Template Function bats::add_uniform_noise(Matrix<T>&, const T, const T)

• Template Function bats::add_uniform_noise(DataSet<T>&, const T, const T)

• Function bats::all_pairs

• Template Function bats::approx_center

• Template Function bats::assign_set_lower

• Template Function bats::assign_set_upper

• Template Function bats::barcode(const Diagram<NT, TM>&, size_t)

• Template Function bats::barcode(const Diagram<NT, TM>&, size_t, flags::divide_conquer)

• Template Function bats::barcode(const Diagram<NT, TM>&, size_t, flags::leftward)

• Template Function bats::barcode(const Diagram<NT, TM>&, size_t, flags::rightward)

• Template Function bats::barcode(const Diagram<NT, std::vector<TM>>&, Args …)

• Template Function bats::barcode_equality

• Template Function bats::barcode_form_divide_conquer

• Template Function bats::barcode_form_leftright

• Template Function bats::barcode_form_rightleft

• Template Function bats::barcode_from_barcode_form

• Function bats::bars_to_pairs

• Template Function bats::binom_to_inds

• Function bats::bivariate_cover

• Template Function bats::Chain(const Filtration<FT, CpxT>&, T)

• Template Function bats::Chain(const Diagram<CpxT, CellularMap>&, T)

• Template Function bats::Chain(const CpxT&, T)

• Template Function bats::Chain(const CpxT&, const CpxT&, T)

• Template Function bats::Chain(const CellularMap&, T)

• Template Function bats::ChainFunctor(const DT&)

• Template Function bats::ChainFunctor(const DT&, TF)

• Template Function bats::circle

• Template Function bats::CompleteFlagFiltration

• Template Function bats::coordinate_projection

• Function bats::Cube(size_t, size_t)

• Function bats::Cube(size_t, size_t, size_t)

• Function bats::Cube(size_t, size_t, size_t, size_t, size_t, size_t, size_t, size_t, size_t)

• Function bats::CubicalMap

• Template Function bats::DGLinearFunctor

• Template Function bats::DiscreteMorozovZigzag

• Template Function bats::DiscreteMorozovZigzagSets

• Template Function bats::dowker_edge_param(const Matrix<T>&, const size_t, const size_t)

• Template Function bats::dowker_edge_param(const Matrix<T>&)

• Template Function bats::dowker_filtration_edges

• Template Function bats::DowkerFiltration(const Matrix<T>&, T, size_t)

• Template Function bats::DowkerFiltration(const DataSet<T>&, const DataSet<T>&, const M&, T, size_t)

• Template Function bats::DowkerFiltration(const Matrix<T>&, const bats::Cover&, T, size_t)

• Template Function bats::DowkerFiltration(const DataSet<T>&, const DataSet<T>&, const M&, const bats::Cover&, T, size_t)

• Template Function bats::EilenbergZilber(const CpxT&, const CpxT&, const CpxT&, const CpxT&, const size_t, T)

• Template Function bats::EilenbergZilber(const CpxT&, const CpxT&, const size_t, T)

• Template Function bats::enclosing_radius

• Template Function bats::euclidean

• Function bats::extension_perm

• Template Function bats::extract_basis_indices(const MT&, const std::vector<size_t>&)

• Template Function bats::extract_basis_indices(const MT&)

• Template Function bats::extract_dimension

• Template Function bats::extract_pairs

• Function bats::filtration_iperm

• Template Function bats::filtration_sortperm(const std::vector<T>&)

• Template Function bats::filtration_sortperm(const std::vector<std::vector<T>>&)

• Function bats::find_parent

• Template Function bats::find_perm_from_vector

• Template Function bats::flag_filtration_edges

• Template Function bats::FlagComplex

• Template Function bats::FlagFiltration

• Template Function bats::FlagFiltration_extension

• Template Function bats::force_repel_rp

• Template Function bats::Freudenthal(size_t, size_t)

• Template Function bats::Freudenthal(size_t, size_t, size_t)

• Template Function bats::Freudenthal(size_t, size_t, size_t, size_t, size_t, size_t, size_t, size_t, size_t)

• Template Function bats::Freudenthal(const CubicalComplex&, size_t, size_t, size_t)

• Function bats::gen_cylinder

• Function bats::get_clearing_inds

• Template Function bats::get_compression_inds

• Template Function bats::get_dM_ZZ_inds

• Template Function bats::get_m

• Template Function bats::get_subset

• Template Function bats::greedy_landmarks

• Template Function bats::greedy_landmarks_hausdorff(const DataSet<T>&, const M&, const size_t)

• Template Function bats::greedy_landmarks_hausdorff(const DataSet<T>&, const M&, const size_t, const size_t)

• Template Function bats::greedy_landmarks_hausdorff(const Matrix<T>&, const size_t)

• Template Function bats::hausdorff_landmarks

• Template Function bats::Hom(const Diagram<DGVectorSpace<TM>, DGLinearMap<TM>>&, bool)

• Template Function bats::Hom(const Diagram<ChainComplex<TM>, ChainMap<TM>>&, size_t)

• Template Function bats::Hom(const Diagram<ChainComplex<TM>, ChainMap<TM>>&, bool)

• Template Function bats::Hom(const Diagram<DGVectorSpace<TM>, DGLinearMap<TM>>&, size_t)

• Function bats::identity_perm

• Template Function bats::increment_m

• Template Function bats::induced_map(const ChainMap<ColumnMatrix<TVec>>&, const ReducedChainComplex<ColumnMatrix<TVec>>&, const ReducedChainComplex<ColumnMatrix<TVec>>&, size_t)

• Template Function bats::induced_map(const ChainMap<ColumnMatrix<TVec>>&, const ReducedCochainComplex<ColumnMatrix<TVec>>&, const ReducedCochainComplex<ColumnMatrix<TVec>>&, size_t)

• Template Function bats::induced_map(const DGLinearMap<ColumnMatrix<TVec>>&, const ReducedDGVectorSpace<ColumnMatrix<TVec>>&, const ReducedDGVectorSpace<ColumnMatrix<TVec>>&, size_t)

• Template Function bats::interval

• Template Function bats::is_left_arrow

• Template Function bats::k_choose_2

• Function bats::k_choose_2_inv

• Template Function bats::kdist

• Template Function bats::Kendall_tau(const std::vector<T>&)

• Template Function bats::Kendall_tau(const std::vector<T>&, const std::vector<T>&)

• Template Function bats::Kendall_tau(const std::vector<std::vector<T>>&)

• Template Function bats::Kendall_tau_inplace

• Template Function bats::Kendall_tau_merge

• Template Function bats::kron_chain_shift

• Template Function bats::kron_chains

• Template Function bats::kron_homology

• Template Function bats::kron_index

• Template Function bats::landmark_cover

• Template Function bats::landmark_eps_cover

• Function bats::linear_cover_intersection_diagram

• Function bats::linear_subset_union_diagram

• Template Function bats::LowerStarFiltration

• Template Function bats::make_edge

• Template Function bats::mayer_vietoris_boundary

• Template Function bats::neighborhood(const VectorView<T>&, const DataSet<T>&, const M&, const T)

• Template Function bats::neighborhood(const VectorView<T>&, const DataSet<T>&, const M&, const size_t)

• Template Function bats::neighborhoods(const DataSet<T>&, const DataSet<T>&, const M&, const T)

• Template Function bats::neighborhoods(const DataSet<T>&, const DataSet<T>&, const M&, const size_t)

• Template Function bats::neighborhoods(const Matrix<T>&, const T)

• Function bats::Nerve(const Diagram<bats::Cover, std::vector<size_t>>&, const size_t)

• Function bats::Nerve(const bats::Cover&, const size_t)

• Template Function bats::normalize_entries

• Template Function bats::operator<

• Template Function bats::operator<<

• Template Function bats::OscillatingRipsZigzagSets

• Template Function bats::pairwise_dist

• Template Function bats::partial_reduce_parallel(ColumnMatrix<TVec>&, const size_t)

• Template Function bats::partial_reduce_parallel(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, const size_t)

• Template Function bats::pass_L_left

• Template Function bats::pass_P_left

• Template Function bats::pass_P_right

• Template Function bats::pass_PL_left

• Template Function bats::pass_U_right

• Template Function bats::pass_UP_right

• Function bats::perm_to_the_end(const size_t&, const size_t&)

• Function bats::perm_to_the_end(const std::vector<size_t>&, const size_t&)

• Template Function bats::print_1D_vectors

• Template Function bats::print_2D_vectors

• Template Function bats::print_filtration_info

• Template Function bats::print_simplex

• Template Function bats::print_summary_of_filtration

• Function bats::prod_ind

• Template Function bats::product_paths(CpxT&, itT, const itT, itT, const itT, std::vector<size_t>&, const size_t)

• Template Function bats::product_paths(CpxT&, itT, const itT, itT, const itT, std::vector<size_t>&, const size_t, std::vector<cell_ind>&)

• Template Function bats::product_space

• Template Function bats::random_landmarks

• Template Function bats::read_point_cloud

• Template Function bats::Reduce(const Filtration<FT, CpxT>&, T, Args …)

• Template Function bats::Reduce(const FilteredChainComplex<T, MT>&, Args …)

• Template Function bats::Reduce(const CpxT&, T, Args …)

• Template Function bats::Reduce(const ChainComplex<MT>&, Args …)

• Template Function bats::reduce_block_dq(ColumnMatrix<TVec>&, const size_t, const size_t, const size_t, const size_t, const size_t)

• Template Function bats::reduce_block_dq(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, const size_t, const size_t, const size_t)

• Template Function bats::reduce_block_sequential(ColumnMatrix<TVec>&, const size_t, const size_t)

• Template Function bats::reduce_block_sequential(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, const size_t, const size_t)

• Template Function bats::reduce_column_extra

• Template Function bats::reduce_column_sparsify

• Template Function bats::reduce_column_standard(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, const size_t, std::unordered_map<size_t, size_t>&, typename TVec::tmp_type&)

• Template Function bats::reduce_column_standard(ColumnMatrix<TVec>&, const size_t, std::unordered_map<size_t, size_t>&, typename TVec::tmp_type&)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&, divide_conquer_flag)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&, bats::standard_reduction_flag)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&, bats::extra_reduction_flag)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, bats::standard_reduction_flag)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, bats::extra_reduction_flag)

• Template Function bats::reduce_matrix(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, divide_conquer_flag)

• Template Function bats::reduce_matrix_clearing(ColumnMatrix<TVec>&, const std::vector<size_t>&, flag)

• Template Function bats::reduce_matrix_clearing(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, const ColumnMatrix<TVec>&, const std::vector<size_t>&, flag)

• Template Function bats::reduce_matrix_compression(ColumnMatrix<TVec>&, const std::vector<bool>&, flag)

• Template Function bats::reduce_matrix_compression(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, const std::vector<bool>&, flag)

• Template Function bats::reduce_matrix_extra(ColumnMatrix<TVec>&)

• Template Function bats::reduce_matrix_extra(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&)

• Template Function bats::reduce_matrix_standard(ColumnMatrix<TVec>&)

• Template Function bats::reduce_matrix_standard(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&)

• Template Function bats::remove_extra_cycles

• Template Function bats::Rips(const Diagram<std::set<size_t>, std::vector<size_t>>&, const DataSet<T>&, const M&, const T, const size_t)

• Template Function bats::Rips(const Diagram<std::set<size_t>, std::vector<size_t>>&, const DataSet<T>&, const M&, const std::vector<T>&, const size_t)

• Template Function bats::rips_edges(std::vector<T>&, std::vector<size_t>&, std::vector<T>&)

• Template Function bats::rips_edges(const DataSet<T>&, const M&, const T)

• Template Function bats::rips_edges(const Matrix<T>&, const T)

• Template Function bats::rips_filtration_edges(const DataSet<T>&, const M&, const T)

• Template Function bats::rips_filtration_edges(const Matrix<T>&, const T)

• Template Function bats::rips_filtration_edges(const DataSet<T>&, const bats::Cover&, const M&, const T)

• Template Function bats::rips_union_find_pairs

• Template Function bats::RipsComplex(const DataSet<T>&, const M&, T, size_t)

• Template Function bats::RipsComplex(const Matrix<T>&, T, size_t)

• Template Function bats::RipsFiltration(const DataSet<T>&, const M&, T, size_t)

• Template Function bats::RipsFiltration(const Matrix<T>&, T, size_t)

• Template Function bats::RipsFiltration(const DataSet<T>&, const bats::Cover&, const M&, T, size_t)

• Template Function bats::RipsFiltration_extension(const DataSet<T>&, const M&, T, size_t)

• Template Function bats::RipsFiltration_extension(const Matrix<T>&, T, size_t)

• Template Function bats::RipsHom

• Template Function bats::sample_cube(const size_t, const size_t)

• Template Function bats::sample_cube(const size_t, const size_t, unsigned)

• Template Function bats::sample_sphere(const size_t, const size_t, unsigned)

• Template Function bats::sample_sphere(const size_t, const size_t)

• Function bats::serpinski_diagram

• Template Function bats::SimplicialMap(const CpxT&, const CpxT&)

• Template Function bats::SimplicialMap(const CpxT&, const CpxT&, const std::vector<size_t>&)

• Template Function bats::sort_edges

• Template Function bats::sort_indexes

• Template Function bats::sparsify_basis(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&, const size_t, std::map<F, size_t>&, typename TVec::tmp_type&)

• Template Function bats::sparsify_basis(ColumnMatrix<TVec>&, ColumnMatrix<TVec>&)

• Template Function bats::StrictRipsCoverFiltration

• Template Function bats::StrictWitnessComplex

• Template Function bats::test_reduce_result

• Template Function bats::TriangulatedProduct(const CpxT&, const CpxT&, const size_t, const size_t)

• Template Function bats::TriangulatedProduct(const CpxT&, const CpxT&, const size_t)

• Template Function bats::TriangulatedProduct(const CpxT&, const CpxT&)

• Template Function bats::type_A_dq_common

• Template Function bats::type_A_dq_EL

• Template Function bats::type_A_dq_EU

• Template Function bats::type_A_leftright_sweep1

• Template Function bats::type_A_leftright_sweep2

• Template Function bats::type_A_rightleft_sweep1

• Template Function bats::type_A_rightleft_sweep2

• Template Function bats::uniform_interval_cover

• Template Function bats::union_find_pairs

• Template Function bats::vertex_inclusion_map

• Template Function bats::witness_edge_param

• Template Function bats::witness_edges(const DataSet<T>&, const DataSet<T>&, const M&)

• Template Function bats::witness_edges(const DataSet<T>&, const DataSet<T>&, const M&, const T)

• Template Function bats::witness_neighborhoods

• Template Function bats::WitnessComplex(const DataSet<T>&, const DataSet<T>&, const M&, const size_t)

• Template Function bats::WitnessComplex(const DataSet<T>&, const DataSet<T>&, const M&, const size_t, const T, const size_t)

• Template Function bats::WitnessFiltration

• Template Function bats::zigzag_levelsets

• Template Function bats::zigzag_toplex

Typedefs

• Typedef bats::Cover

• Typedef bats::Matrix

Variables

• Variable bats::NO_IND