mfGeometry: R6 Class implementing manifold geometries
In Almond-S/manifoldboost: Boosting Regression Models for Manifold Valued Data
mfGeometry R Documentation
R6 Class implementing manifold geometries
Description
R6 Class implementing manifold geometries
R6 Class implementing manifold geometries
Details
An abstract mfGeometry class implementing a set of methods, including
e.g. Exp- and Log-mappings, that are needed to define mfboost families
in a concise and modular way.
The arguments of the methods are vectors, matrices
or arrays possibly holding additional attributes. Besides these methods, objects
of class mfGeometry offer an active slot for the 'pole' which serves
as prototype for elements of the manifold. Children of this class
specify the geometry of interest, such as mfGeomEuclidean,
mfGeomSphere, mfGeomPlanarShape, and
mfGeomPlanarSizeShape.
Active bindings
y_slot for a data object in the internal format
pole_slot for a data object in the internal format
weights_slot for inner product weights in the internal format
Methods
Public methods
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Method structure()
structure a vector containing the elements of the response
y in long format in the internal format of the geometry.
Usage
mfGeometry$structure(y)
Arguments
ya numeric vector containing the elements of an object y in long format
Method unstructure()
inverse operation of structure.
Usage
mfGeometry$unstructure(y_)
Arguments
y_an object in the internal format of the geometry
Method unstructure_weights()
convert internal inner product weights to a weight vector
matching the un-structered response y in long format.
Usage
mfGeometry$unstructure_weights(weights_)
Arguments
weights_inner product weights in the internal format
Method align()
a function aligning y_ to y0_ primarly intended
for quotient geometries.
Usage
mfGeometry$align(y_, y0_ = private$.pole_)
Arguments
y_an object in the internal format of the geometry
y0_an object in the internal format of the geometry
Method register()
a function registering y_ to a proper subset, say to
a subspace or an embedded submanifold.
Usage
mfGeometry$register(y_)
Arguments
y_an object in the internal format of the geometry
Method distance()
computes the distance or a vector of distances between objects.
Usage
mfGeometry$distance(y0_, y1_, ...)
Arguments
y0_an object in the internal format of the geometry
y1_an object in the internal format of the geometry
...other arguments.
Method exp()
the Riemannian Exp map mapping a tangent vector v_
at y_ to the manifold.
Usage
mfGeometry$exp(v_, y0_ = private$.pole_, ...)
Arguments
v_an object repesenting a tangent vector (internal format)
y0_an object in the internal format of the geometry
...other arguments.
Method log()
the inverse of the Riemannian Exp map.
Usage
mfGeometry$log(y_, y0_ = private$.pole_, ...)
Arguments
y_an object in the internal format of the geometry
y0_an object in the internal format of the geometry
...other arguments.
Method transport()
parallel transport of a tangent vector v0_
at y0_ to the tangent space at y1_.
Usage
mfGeometry$transport(v0_, y0_, y1_, ...)
Arguments
v0_an object repesenting a tangent vector (internal format)
y0_an object in the internal format of the geometry
y1_an object in the internal format of the geometry
...other arguments.
Method innerprod()
computes the inner product or a vector of inner products
between objects.
Usage
mfGeometry$innerprod(v0_, v1_ = v0_, ...)
Arguments
v0_an object repesenting a tangent vector (internal format)
v1_an object repesenting a tangent vector (internal format)
...other arguments.
Method get_normal()
returns the normal vector (in unstructured format) to the
tangent space at a point y0_ considered as a linear subspace.
Usage
mfGeometry$get_normal(y0_ = private$.pole_, ...)
Arguments
y0_an object in the internal format of the geometry
...other arguments.
Method validate()
function for validating structure of internal object y_.
Usage
mfGeometry$validate(y_, ...)
Arguments
y_an object in the internal format of the geometry
...other arguments.
Method clone()
The objects of this class are cloneable with this method.
Usage
mfGeometry$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Almond-S/manifoldboost documentation built on June 23, 2022, 11:06 a.m.
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| mfGeometry | R Documentation |
R6 Class implementing manifold geometries
Description
R6 Class implementing manifold geometries
R6 Class implementing manifold geometries
Details
An abstract mfGeometry class implementing a set of methods, including
e.g. Exp- and Log-mappings, that are needed to define mfboost families
in a concise and modular way.
The arguments of the methods are vectors, matrices
or arrays possibly holding additional attributes. Besides these methods, objects
of class mfGeometry offer an active slot for the 'pole' which serves
as prototype for elements of the manifold. Children of this class
specify the geometry of interest, such as mfGeomEuclidean,
mfGeomSphere, mfGeomPlanarShape, and
mfGeomPlanarSizeShape.
Active bindings
y_slot for a data object in the internal format
pole_slot for a data object in the internal format
weights_slot for inner product weights in the internal format
Methods
Public methods
Method structure()
structure a vector containing the elements of the response
y in long format in the internal format of the geometry.
Usage
mfGeometry$structure(y)
Arguments
ya numeric vector containing the elements of an object y in long format
Method unstructure()
inverse operation of structure.
Usage
mfGeometry$unstructure(y_)
Arguments
y_an object in the internal format of the geometry
Method unstructure_weights()
convert internal inner product weights to a weight vector
matching the un-structered response y in long format.
Usage
mfGeometry$unstructure_weights(weights_)
Arguments
weights_inner product weights in the internal format
Method align()
a function aligning y_ to y0_ primarly intended
for quotient geometries.
Usage
mfGeometry$align(y_, y0_ = private$.pole_)
Arguments
y_an object in the internal format of the geometry
y0_an object in the internal format of the geometry
Method register()
a function registering y_ to a proper subset, say to
a subspace or an embedded submanifold.
Usage
mfGeometry$register(y_)
Arguments
y_an object in the internal format of the geometry
Method distance()
computes the distance or a vector of distances between objects.
Usage
mfGeometry$distance(y0_, y1_, ...)
Arguments
y0_an object in the internal format of the geometry
y1_an object in the internal format of the geometry
...other arguments.
Method exp()
the Riemannian Exp map mapping a tangent vector v_
at y_ to the manifold.
Usage
mfGeometry$exp(v_, y0_ = private$.pole_, ...)
Arguments
v_an object repesenting a tangent vector (internal format)
y0_an object in the internal format of the geometry
...other arguments.
Method log()
the inverse of the Riemannian Exp map.
Usage
mfGeometry$log(y_, y0_ = private$.pole_, ...)
Arguments
y_an object in the internal format of the geometry
y0_an object in the internal format of the geometry
...other arguments.
Method transport()
parallel transport of a tangent vector v0_
at y0_ to the tangent space at y1_.
Usage
mfGeometry$transport(v0_, y0_, y1_, ...)
Arguments
v0_an object repesenting a tangent vector (internal format)
y0_an object in the internal format of the geometry
y1_an object in the internal format of the geometry
...other arguments.
Method innerprod()
computes the inner product or a vector of inner products between objects.
Usage
mfGeometry$innerprod(v0_, v1_ = v0_, ...)
Arguments
v0_an object repesenting a tangent vector (internal format)
v1_an object repesenting a tangent vector (internal format)
...other arguments.
Method get_normal()
returns the normal vector (in unstructured format) to the
tangent space at a point y0_ considered as a linear subspace.
Usage
mfGeometry$get_normal(y0_ = private$.pole_, ...)
Arguments
y0_an object in the internal format of the geometry
...other arguments.
Method validate()
function for validating structure of internal object y_.
Usage
mfGeometry$validate(y_, ...)
Arguments
y_an object in the internal format of the geometry
...other arguments.
Method clone()
The objects of this class are cloneable with this method.
Usage
mfGeometry$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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