Sparse Rips complex data structure. More...
#include </home/gailuron/workspace/gudhi/gudhi-devel/build/gudhi.3.5.0/include/gudhi/Sparse_rips_complex.h>
Public Member Functions | |
template<typename RandomAccessPointRange , typename Distance > | |
Sparse_rips_complex (const RandomAccessPointRange &points, Distance distance, double const epsilon, Filtration_value const mini=-std::numeric_limits< Filtration_value >::infinity(), Filtration_value const 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 const epsilon, Filtration_value const mini=-std::numeric_limits< Filtration_value >::infinity(), Filtration_value const 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 const 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... | |
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.
Filtration_value | is the type used to store the filtration values of the simplicial complex. |
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inline |
Sparse_rips_complex constructor from a list of points.
[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. |
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inline |
Sparse_rips_complex constructor from a distance matrix.
[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. |
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inline |
Fills the simplicial complex with the sparse Rips graph and expands it with all the cliques, stopping at a given maximal dimension.
SimplicialComplexForRips | must meet SimplicialComplexForRips concept. |
[in] | complex | the complex to fill |
[in] | dim_max | maximal dimension of the simplicial complex. |
std::invalid_argument | In debug mode, if complex.num_vertices() does not return 0. |
GUDHI Version 3.5.0 - C++ library for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding. - Copyright : MIT | Generated on Thu Jan 13 2022 08:34:28 for GUDHI by Doxygen 1.9.2 |