mfGeomProduct: A general product geometry
In Almond-S/manifoldboost: Boosting Regression Models for Manifold Valued Data
mfGeomProduct R Documentation
A general product geometry
Description
A general product geometry
A general product geometry
Details
An mfGeometry class implementing a product geometry in an abstract
general way. While there might be more efficient implementations using the
particular structure of your geometry of interest, this should work for
products of any mfGeometries.
Super class
manifoldboost::mfGeometry -> mfGeomProduct
Public fields
mfGeom_defaultan mfGeometry object implementing the default
geometry of a component of the product space.
Active bindings
y_return lists of respective elements in the components.
y_ can be specified as a list of mfGeometry objects constituting
the components of the product geometry.
pole_return lists of respective elements in the components.
weights_return lists of respective elements in the components.
mfGeom_classesreturn a list of the classes of y_ (read only).
Methods
Public methods
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Inherited methods
Method new()
Initialize product geometry with each
component the mfGeom_default based on the
data containing the variables for y_
specified in the formula.
Usage
mfGeomProduct$new(mfGeom_default, data, formula)
Arguments
mfGeom_defaultmfGeometry object carrying the
component geometry.
datacontaining required variables.
formulaformula containing interpreted
via mfInterpret_formula) and indicating, in particular,
the ID variable for splitting observations in the product
components.
Method slice()
subset product geometry to specified components.
Make sure to clone the product geometry first if
complete geometry should be preserved.
Usage
mfGeomProduct$slice(which)
Arguments
whichintegers or character strings indicating
which elements of y_ should be selected.
Method structure()
bring y into the right order to
split and pass it to the component geometries.
Usage
mfGeomProduct$structure(y)
Arguments
ya list of y elements of the component manifolds in an
unstructured 'flattened' way
Method unstructure()
unstructure y_ in the component geometries
and arrange it into the right order.
Usage
mfGeomProduct$unstructure(y_)
Arguments
y_a list of objects living in the component manifolds
Method unstructure_weights()
unstructure weights_ in the component geometries
and arrange it into the right order.
Usage
mfGeomProduct$unstructure_weights(weights_)
Arguments
weights_list of numeric vectors of inner product weights.
Method structure_weights()
bring weights into the right order to
split and pass it to the component geometries.
Usage
mfGeomProduct$structure_weights(weights)
Arguments
weightsnumeric vector of inner product weights matching the y
as a numeric vector.
Method align()
component-wise alignment.
Usage
mfGeomProduct$align(y_, y0_, ...)
Arguments
y_a list of objects living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method register()
component-wise registration.
Usage
mfGeomProduct$register(y_, ...)
Arguments
y_a list of objects living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method register_v()
component-wise registration.
Usage
mfGeomProduct$register_v(v_, y0_, ...)
Arguments
v_a list of tangent vectors living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method distance()
compute vector of distances in component
geometries.
Usage
mfGeomProduct$distance(y0_, y1_, ...)
Arguments
y0_a list of objects living in the component manifolds
y1_a list of objects living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method exp()
loop over Exp-maps in the component
geometries.
Usage
mfGeomProduct$exp(v_, y0_, ...)
Arguments
v_a list of tangent vectors living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method log()
loop over Log-maps in the component
geometries.
Usage
mfGeomProduct$log(y_, y0_, ...)
Arguments
y_a list of objects living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method transport()
loop over parallel transports in the component
geometries.
Usage
mfGeomProduct$transport(v0_, y0_, y1_, ...)
Arguments
v0_a list of tangent vectors living in the component manifolds
y0_a list of objects living in the component manifolds
y1_a list of objects living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method innerprod()
compute vector of inner products in the
component geometries. An inner product on the product
space can be obtained as a scalar product of the
returned vector.
Usage
mfGeomProduct$innerprod(v0_, v1_ = v0_, ...)
Arguments
v0_a list of tangent vectors living in the component manifolds
v1_a list of tangent vectors living in the component manifolds
...other arguments passed to underlying mfGeometry.
Method plot()
loop over individual plots of the components.
Usage
mfGeomProduct$plot(y_ = self$y_, y0_ = self$pole_, main = names(y_), ...)
Arguments
y_a list of objects living in the component manifolds
y0_a list of objects living in the component manifolds
mainvector of plot titles
...other arguments passed to underlying mfGeometry.
Method get_normal()
Obtain "design matrix" of tangent space normal vectors in
unstructured long format, arranging rows into the right
order after evaluating it on the components.
Usage
mfGeomProduct$get_normal(y0_ = self$pole_, weighted = FALSE)
Arguments
y0_a list of objects living in the component manifolds
weightedlogical, should inner product weights be pre-multiplied to
normal vectors?
Method validate()
loop of validation functions of component geometries.
Usage
mfGeomProduct$validate(y_)
Arguments
y_a list of objects living in the component manifolds
Method clone()
The objects of this class are cloneable with this method.
Usage
mfGeomProduct$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Almond-S/manifoldboost documentation built on June 23, 2022, 11:06 a.m.
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| mfGeomProduct | R Documentation |
A general product geometry
Description
A general product geometry
A general product geometry
Details
An mfGeometry class implementing a product geometry in an abstract
general way. While there might be more efficient implementations using the
particular structure of your geometry of interest, this should work for
products of any mfGeometries.
Super class
manifoldboost::mfGeometry -> mfGeomProduct
Public fields
mfGeom_defaultan
mfGeometryobject implementing the default geometry of a component of the product space.
Active bindings
y_return lists of respective elements in the components.
y_can be specified as a list ofmfGeometryobjects constituting the components of the product geometry.pole_return lists of respective elements in the components.
weights_return lists of respective elements in the components.
mfGeom_classesreturn a list of the classes of
y_(read only).
Methods
Public methods
Inherited methods
Method new()
Initialize product geometry with each
component the mfGeom_default based on the
data containing the variables for y_
specified in the formula.
Usage
mfGeomProduct$new(mfGeom_default, data, formula)
Arguments
mfGeom_defaultmfGeometryobject carrying the component geometry.datacontaining required variables.
formulaformula containing interpreted via
mfInterpret_formula) and indicating, in particular, the ID variable for splitting observations in the product components.
Method slice()
subset product geometry to specified components. Make sure to clone the product geometry first if complete geometry should be preserved.
Usage
mfGeomProduct$slice(which)
Arguments
whichintegers or character strings indicating which elements of
y_should be selected.
Method structure()
bring y into the right order to
split and pass it to the component geometries.
Usage
mfGeomProduct$structure(y)
Arguments
ya list of
yelements of the component manifolds in an unstructured 'flattened' way
Method unstructure()
unstructure y_ in the component geometries
and arrange it into the right order.
Usage
mfGeomProduct$unstructure(y_)
Arguments
y_a list of objects living in the component manifolds
Method unstructure_weights()
unstructure weights_ in the component geometries
and arrange it into the right order.
Usage
mfGeomProduct$unstructure_weights(weights_)
Arguments
weights_list of numeric vectors of inner product weights.
Method structure_weights()
bring weights into the right order to
split and pass it to the component geometries.
Usage
mfGeomProduct$structure_weights(weights)
Arguments
weightsnumeric vector of inner product weights matching the
yas a numeric vector.
Method align()
component-wise alignment.
Usage
mfGeomProduct$align(y_, y0_, ...)
Arguments
y_a list of objects living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method register()
component-wise registration.
Usage
mfGeomProduct$register(y_, ...)
Arguments
y_a list of objects living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method register_v()
component-wise registration.
Usage
mfGeomProduct$register_v(v_, y0_, ...)
Arguments
v_a list of tangent vectors living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method distance()
compute vector of distances in component geometries.
Usage
mfGeomProduct$distance(y0_, y1_, ...)
Arguments
y0_a list of objects living in the component manifolds
y1_a list of objects living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method exp()
loop over Exp-maps in the component geometries.
Usage
mfGeomProduct$exp(v_, y0_, ...)
Arguments
v_a list of tangent vectors living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method log()
loop over Log-maps in the component geometries.
Usage
mfGeomProduct$log(y_, y0_, ...)
Arguments
y_a list of objects living in the component manifolds
y0_a list of objects living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method transport()
loop over parallel transports in the component geometries.
Usage
mfGeomProduct$transport(v0_, y0_, y1_, ...)
Arguments
v0_a list of tangent vectors living in the component manifolds
y0_a list of objects living in the component manifolds
y1_a list of objects living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method innerprod()
compute vector of inner products in the component geometries. An inner product on the product space can be obtained as a scalar product of the returned vector.
Usage
mfGeomProduct$innerprod(v0_, v1_ = v0_, ...)
Arguments
v0_a list of tangent vectors living in the component manifolds
v1_a list of tangent vectors living in the component manifolds
...other arguments passed to underlying
mfGeometry.
Method plot()
loop over individual plots of the components.
Usage
mfGeomProduct$plot(y_ = self$y_, y0_ = self$pole_, main = names(y_), ...)
Arguments
y_a list of objects living in the component manifolds
y0_a list of objects living in the component manifolds
mainvector of plot titles
...other arguments passed to underlying
mfGeometry.
Method get_normal()
Obtain "design matrix" of tangent space normal vectors in unstructured long format, arranging rows into the right order after evaluating it on the components.
Usage
mfGeomProduct$get_normal(y0_ = self$pole_, weighted = FALSE)
Arguments
y0_a list of objects living in the component manifolds
weightedlogical, should inner product weights be pre-multiplied to normal vectors?
Method validate()
loop of validation functions of component geometries.
Usage
mfGeomProduct$validate(y_)
Arguments
y_a list of objects living in the component manifolds
Method clone()
The objects of this class are cloneable with this method.
Usage
mfGeomProduct$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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