Abstract Class for Open Set Manifolds

Class for manifolds that are open sets of a vector space. In this case, tangent vectors are identified with vectors of the ambient space.

See also

SPDMatrix

Author

Nicolas Guigui and Nina Miolane

Super classes

rgeomstats::PythonClass -> rgeomstats::Manifold -> OpenSet

Public fields

ambient_space

An object of class VectorSpace specifying the ambient space.

Methods

Public methods

• OpenSet$new()

• OpenSet$projection()

• OpenSet$clone()

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 OpenSet class constructor.

Usage

OpenSet$new(dim, ambient_space, ..., py_cls = NULL)

Arguments

dim

An integer value specifying the dimension of the manifold.

ambient_space

An object of class VectorSpace specifying the ambient space.

...

Extra arguments to be passed to parent class constructors. See Manifold class.

py_cls

A Python object of class OpenSet. Defaults to NULL in which case it is instantiated on the fly using the other input arguments.

Returns

An object of class OpenSet.

---

Method projection()

Project a point in the ambient space onto the manifold.

Usage

OpenSet$projection(point)

Arguments

point

A numeric array of shape \([\dots \times \{\mathrm{dim}\}]\) specifying one or more vectors in the ambient space of the manifold.

Returns

A numeric array of the same shape storing the corresponding projections onto the manifold.

Examples

if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  spd3$projection(diag(1, 3))
}

---

Method clone()

The objects of this class are cloneable with this method.

Usage

OpenSet$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

## ------------------------------------------------
## Method `OpenSet$projection`
## ------------------------------------------------

if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  spd3$projection(diag(1, 3))
}