TangentialComplex: R6 Class for Tangential Complex
In rgudhi: An Interface to the GUDHI Library for Topological Data Analysis
TangentialComplex R Documentation
R6 Class for Tangential Complex
Description
A Tangential Delaunay complex is a simplicial complex designed
to reconstruct a k-dimensional manifold embedded in
d-dimensional Euclidean space. The input is a point sample coming
from an unknown manifold. The running time depends only linearly on the
extrinsic dimension d and exponentially on the intrinsic dimension
k.
Details
The TangentialComplex class represents a tangential complex. After
the computation of the complex, an optional post-processing called
perturbation can be run to attempt to remove inconsistencies.
Super class
rgudhi::PythonClass -> TangentialComplex
Methods
Public methods
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Inherited methods
Method new()
TangentialComplex constructor.
Usage
TangentialComplex$new(points, intrinsic_dim = NULL)
Arguments
pointsEither a character string specifying the path to an OFF
file which the points can be read from or a numeric matrix or list of
numeric vectors specifying the points directly.
intrinsic_dimAn integer value specifying the intrinsic dimension
of the manifold. This is nedded when points are provided as a numeric
matrix or a list of numeric vectors. Defaults to NULL.
Returns
A TangentialComplex object storing the tangential
complex.
Method compute_tangential_complex()
This function computes the tangential complex.
Usage
TangentialComplex$compute_tangential_complex()
Details
In debug mode, it may raise a ValueError if the computed star
dimension is too low. Try to set a bigger maximal edge length value via
the $set_max_squared_edge_length() method if this happens.
Returns
The updated TangentialComplex class itself
invisibly.
Method create_simplex_tree()
Exports the complex into a simplex tree.
Usage
TangentialComplex$create_simplex_tree()
Returns
A SimplexTree object storing the computed simplex
tree.
Method get_point()
This function returns the point corresponding to a given
vertex from the SimplexTree.
Usage
TangentialComplex$get_point(vertex)
Arguments
vertexAn integer value specifying the desired vertex.
Returns
A numeric vector storing the point corresponding to the input
vertex.
Method num_inconsistent_simplices()
Usage
TangentialComplex$num_inconsistent_simplices()
Returns
An integer value storing the number of inconsistent simplicies.
Method num_inconsistent_stars()
Usage
TangentialComplex$num_inconsistent_stars()
Returns
An integer value storing the number of stars containing at least
one inconsistent simplex.
Method num_simplices()
Usage
TangentialComplex$num_simplices()
Returns
An integer value storing the total number of simplices in stars
(including duplicates that appear in several stars).
Method num_vertices()
Usage
TangentialComplex$num_vertices()
Returns
An integer value storing the number of vertices.
Method set_max_squared_edge_length()
Sets the maximal possible squared edge length for the edges
in the triangulations.
Usage
TangentialComplex$set_max_squared_edge_length(max_squared_edge_length)
Arguments
max_squared_edge_lengthA numeric value specifying the maximal
possible squared edge length.
Details
If the maximal edge length value is too low, the
$compute_tangential_complex() method will throw an exception in debug
mode.
Returns
The updated TangentialComplex class itself
invisibly.
Method clone()
The objects of this class are cloneable with this method.
Usage
TangentialComplex$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Clément Jamin
See Also
Other filtrations and reconstructions:
AlphaComplex,
RipsComplex,
WitnessComplex
Examples
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
st <- tc$compute_tangential_complex()$create_simplex_tree()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
st <- tc$compute_tangential_complex()$create_simplex_tree()
tc$get_point(1)
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_inconsistent_simplices()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_inconsistent_stars()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_simplices()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_vertices()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$set_max_squared_edge_length(1)
rgudhi documentation built on March 31, 2023, 11:38 p.m.
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| TangentialComplex | R Documentation |
R6 Class for Tangential Complex
Description
A Tangential Delaunay complex is a simplicial complex designed
to reconstruct a k-dimensional manifold embedded in
d-dimensional Euclidean space. The input is a point sample coming
from an unknown manifold. The running time depends only linearly on the
extrinsic dimension d and exponentially on the intrinsic dimension
k.
Details
The TangentialComplex class represents a tangential complex. After the computation of the complex, an optional post-processing called perturbation can be run to attempt to remove inconsistencies.
Super class
rgudhi::PythonClass -> TangentialComplex
Methods
Public methods
Inherited methods
Method new()
TangentialComplex constructor.
Usage
TangentialComplex$new(points, intrinsic_dim = NULL)
Arguments
pointsEither a character string specifying the path to an OFF file which the points can be read from or a numeric matrix or list of numeric vectors specifying the points directly.
intrinsic_dimAn integer value specifying the intrinsic dimension of the manifold. This is nedded when points are provided as a numeric matrix or a list of numeric vectors. Defaults to
NULL.
Returns
A TangentialComplex object storing the tangential
complex.
Method compute_tangential_complex()
This function computes the tangential complex.
Usage
TangentialComplex$compute_tangential_complex()
Details
In debug mode, it may raise a ValueError if the computed star
dimension is too low. Try to set a bigger maximal edge length value via
the $set_max_squared_edge_length() method if this happens.
Returns
The updated TangentialComplex class itself
invisibly.
Method create_simplex_tree()
Exports the complex into a simplex tree.
Usage
TangentialComplex$create_simplex_tree()
Returns
A SimplexTree object storing the computed simplex
tree.
Method get_point()
This function returns the point corresponding to a given
vertex from the SimplexTree.
Usage
TangentialComplex$get_point(vertex)
Arguments
vertexAn integer value specifying the desired vertex.
Returns
A numeric vector storing the point corresponding to the input vertex.
Method num_inconsistent_simplices()
Usage
TangentialComplex$num_inconsistent_simplices()
Returns
An integer value storing the number of inconsistent simplicies.
Method num_inconsistent_stars()
Usage
TangentialComplex$num_inconsistent_stars()
Returns
An integer value storing the number of stars containing at least one inconsistent simplex.
Method num_simplices()
Usage
TangentialComplex$num_simplices()
Returns
An integer value storing the total number of simplices in stars (including duplicates that appear in several stars).
Method num_vertices()
Usage
TangentialComplex$num_vertices()
Returns
An integer value storing the number of vertices.
Method set_max_squared_edge_length()
Sets the maximal possible squared edge length for the edges in the triangulations.
Usage
TangentialComplex$set_max_squared_edge_length(max_squared_edge_length)
Arguments
max_squared_edge_lengthA numeric value specifying the maximal possible squared edge length.
Details
If the maximal edge length value is too low, the
$compute_tangential_complex() method will throw an exception in debug
mode.
Returns
The updated TangentialComplex class itself
invisibly.
Method clone()
The objects of this class are cloneable with this method.
Usage
TangentialComplex$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Clément Jamin
See Also
Other filtrations and reconstructions:
AlphaComplex,
RipsComplex,
WitnessComplex
Examples
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
st <- tc$compute_tangential_complex()$create_simplex_tree()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
st <- tc$compute_tangential_complex()$create_simplex_tree()
tc$get_point(1)
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_inconsistent_simplices()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_inconsistent_stars()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_simplices()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$compute_tangential_complex()
tc$num_vertices()
X <- seq_circle(10)
tc <- TangentialComplex$new(points = X, intrinsic_dim = 1)
tc$set_max_squared_edge_length(1)
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