LevelSet {rgeomstats} | R Documentation |
Abstract Class for Level Set Manifolds
Description
Class for manifolds embedded in a vector space by a submersion.
Super classes
rgeomstats::PythonClass
-> rgeomstats::Manifold
-> LevelSet
Public fields
embedding_space
An object of class
VectorSpace
specifying the embedding space.embedding_metric
???
submersion
???
value
???
tangent_submersion
???
Methods
Public methods
Inherited methods
rgeomstats::PythonClass$get_python_class()
rgeomstats::PythonClass$set_python_class()
rgeomstats::Manifold$belongs()
rgeomstats::Manifold$is_tangent()
rgeomstats::Manifold$random_point()
rgeomstats::Manifold$random_tangent_vec()
rgeomstats::Manifold$regularize()
rgeomstats::Manifold$set_metric()
rgeomstats::Manifold$to_tangent()
Method new()
The LevelSet
class constructor.
Usage
LevelSet$new( dim, embedding_space, submersion, value, tangent_submersion, default_coords_type = "intrinsic", ..., py_cls = NULL )
Arguments
dim
An integer value specifying the dimension of the manifold.
embedding_space
An object of class
VectorSpace
specifying the embedding space.submersion
???
value
???
tangent_submersion
???
default_coords_type
A string specifying the coordinate type. Choices are
extrinsic
orintrinsic
. Defaults tointrinsic
....
Extra arguments to be passed to parent class constructors. See
Manifold
class.py_cls
A Python object of class
LevelSet
. Defaults toNULL
in which case it is instantiated on the fly using the other input arguments.
Returns
An object of class LevelSet
.
Method intrinsic_to_extrinsic_coords()
Converts from intrinsic to extrinsic coordinates.
Usage
LevelSet$intrinsic_to_extrinsic_coords(point_intrinsic)
Arguments
point_intrinsic
A numeric array of shape
dim
specifying a point in the embedded manifold in intrinsic coordinates.
Returns
A numeric array of shape dim_embedding
representing the same
point in the embedded manifold in extrinsic coordinates.
Method extrinsic_to_intrinsic_coords()
Converts from extrinsic to intrinsic coordinates.
Usage
LevelSet$extrinsic_to_intrinsic_coords(point_extrinsic)
Arguments
point_extrinsic
A numeric array of shape
dim_embedding
specifying a point in the embedded manifold in extrinsic coordinates, i.E. in the coordinates of the embedding manifold.
Returns
A numeric array of shape dim
representing the same point in the
embedded manifold in intrinsic coordinates.
Method projection()
Projects a point in embedding manifold on embedded manifold.
Usage
LevelSet$projection(point)
Arguments
point
A numeric array of shape
dim_embedding
specifying a point in the embedding manifold.
Returns
A numeric array of shape dim_embedding
storing the projected
point.
Method clone()
The objects of this class are cloneable with this method.
Usage
LevelSet$clone(deep = FALSE)
Arguments
deep
Whether to make a deep clone.
Author(s)
Nicolas Guigui and Nina Miolane