 Gudhi::rips_complex::Sparse_rips_complex< Filtration_value > Class Template Reference

Sparse Rips complex data structure. More...

## Public Member Functions

template<typename RandomAccessPointRange , typename Distance >
Sparse_rips_complex (const RandomAccessPointRange &points, Distance distance, double epsilon, Filtration_value mini=-std::numeric_limits< Filtration_value >::infinity(), Filtration_value maxi=std::numeric_limits< Filtration_value >::infinity())
Sparse_rips_complex constructor from a list of points. More...

template<typename DistanceMatrix >
Sparse_rips_complex (const DistanceMatrix &distance_matrix, double epsilon, Filtration_value mini=-std::numeric_limits< Filtration_value >::infinity(), Filtration_value maxi=std::numeric_limits< Filtration_value >::infinity())
Sparse_rips_complex constructor from a distance matrix. More...

template<typename SimplicialComplexForRips >
void create_complex (SimplicialComplexForRips &complex, int dim_max)
Fills the simplicial complex with the sparse Rips graph and expands it with all the cliques, stopping at a given maximal dimension. More...

## Detailed Description

### template<typename Filtration_value> class Gudhi::rips_complex::Sparse_rips_complex< Filtration_value >

Sparse Rips complex data structure.

This class is used to construct a sparse $$(1+O(\epsilon))$$-approximation of Rips_complex, i.e. a filtered simplicial complex that is multiplicatively $$(1+O(\epsilon))$$-interleaved with the Rips filtration. More precisely, this is a $$(1,\frac{1}{1-\epsilon}$$-interleaving.

Template Parameters
 Filtration_value is the type used to store the filtration values of the simplicial complex.

## ◆ Sparse_rips_complex() [1/2]

template<typename Filtration_value >
template<typename RandomAccessPointRange , typename Distance >
 Gudhi::rips_complex::Sparse_rips_complex< Filtration_value >::Sparse_rips_complex ( const RandomAccessPointRange & points, Distance distance, double epsilon, Filtration_value mini = -std::numeric_limits::infinity(), Filtration_value maxi = std::numeric_limits::infinity() )
inline

Sparse_rips_complex constructor from a list of points.

Parameters
 [in] points Range of points. [in] distance Distance function that returns a Filtration_value from 2 given points. [in] epsilon Approximation parameter. epsilon must be positive. [in] mini Minimal filtration value. Ignore anything below this scale. This is a less efficient version of Gudhi::subsampling::sparsify_point_set(). [in] maxi Maximal filtration value. Ignore anything above this scale.

## ◆ Sparse_rips_complex() [2/2]

template<typename Filtration_value >
template<typename DistanceMatrix >
 Gudhi::rips_complex::Sparse_rips_complex< Filtration_value >::Sparse_rips_complex ( const DistanceMatrix & distance_matrix, double epsilon, Filtration_value mini = -std::numeric_limits::infinity(), Filtration_value maxi = std::numeric_limits::infinity() )
inline

Sparse_rips_complex constructor from a distance matrix.

Parameters
 [in] distance_matrix Range of range of distances. distance_matrix[i][j] returns the distance between points $$i$$ and $$j$$ as long as $$0 \leqslant j < i \leqslant distance\_matrix.size().$$ [in] epsilon Approximation parameter. epsilon must be positive. [in] mini Minimal filtration value. Ignore anything below this scale. This is a less efficient version of Gudhi::subsampling::sparsify_point_set(). [in] maxi Maximal filtration value. Ignore anything above this scale.

## ◆ create_complex()

template<typename Filtration_value >
template<typename SimplicialComplexForRips >
 void Gudhi::rips_complex::Sparse_rips_complex< Filtration_value >::create_complex ( SimplicialComplexForRips & complex, int dim_max )
inline

Fills the simplicial complex with the sparse Rips graph and expands it with all the cliques, stopping at a given maximal dimension.

Template Parameters
 SimplicialComplexForRips must meet SimplicialComplexForRips concept.
Parameters
 [in] complex the complex to fill [in] dim_max maximal dimension of the simplicial complex.
Exceptions
 std::invalid_argument In debug mode, if complex.num_vertices() does not return 0.

The documentation for this class was generated from the following file:
 GUDHI  Version 3.4.1  - C++ library for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding.  - Copyright : MIT Generated on Fri Jan 22 2021 09:41:16 for GUDHI by Doxygen 1.8.13