Package 'rgeomstats'

Title: Interface to 'Geomstats'
Description: Provides an interface to the Python package 'Geomstats' authored by Miolane et al. (2020) <arXiv:2004.04667>.
Authors: Aymeric Stamm [aut, cre] , Nicolas Guigui [ctb] (Author of the Geomstats Python package, <https://orcid.org/0000-0002-7901-0732>), Alice Le Brigant [ctb] (Author of the Geomstats Python package, <https://orcid.org/0000-0002-8055-4753>), Johan Mathe [ctb] (Author of the Geomstats Python package), Nina Miolane [ctb] (Author of the Geomstats Python package, <https://orcid.org/0000-0002-1200-9024>), Xavier Pennec [ctb] (Author of the Geomstats Python package, <https://orcid.org/0000-0002-6617-7664>), Luis Pereira [ctb] (Author of the Geomstats Python package), Yann Thanwerdas [ctb] (Author of the Geomstats Python package, <https://orcid.org/0000-0002-9351-6318>)
Maintainer: Aymeric Stamm <[email protected]>
License: MIT + file LICENSE
Version: 0.0.1.9000
Built: 2024-10-26 03:40:03 UTC
Source: https://github.com/lmjl-alea/rgeomstats

Help Index

Class for N-Fold Product Manifolds

Description

Class for an nn-fold product manifold MnM^n. It defines a manifold as the product manifold of nn copies of a given base manifold MM.

Super classes

rgeomstats::PythonClass -> rgeomstats::Manifold -> NFoldManifold

Methods

Public methods

Inherited methods

Method new()

The NFoldManifold class constructor.

Usage
NFoldManifold$new(
  base_manifold,
  n_copies,
  metric = NULL,
  default_coords_type = "intrinsic",
  py_cls = NULL
)
Arguments
base_manifold

An R6::R6Class specifying the base manifold to copy.

n_copies

An integer value specifying the number of replication of the base manifold.

metric

An R6::R6Class specifying the base metric to use. Defaults to NULL which uses the Riemannian metric.

default_coords_type

A string specifying the coordinate type. Choices are "intrinsic" or "extrinsic". Defaults to "intrinsic".

py_cls

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

Returns

A NFoldManifold R6::R6Class object.

Examples
if (reticulate::py_module_available("geomstats")) {
  nfm <- NFoldManifold$new(
    base_manifold = SPDMatrix(n = 3),
    n_copies = 3
  )
  nfm
}

Method clone()

The objects of this class are cloneable with this method.

Usage
NFoldManifold$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Author(s)

Nicolas Guigui

Examples

## ------------------------------------------------
## Method `NFoldManifold$new`
## ------------------------------------------------

if (reticulate::py_module_available("geomstats")) {
  nfm <- NFoldManifold$new(
    base_manifold = SPDMatrix(n = 3),
    n_copies = 3
  )
  nfm
}

Class for the Manifold of Symmetric Positive Definite Matrices

Description

This function generates an instance of the class for the manifold of symmetric positive definite matrices SPD(n)\mathrm{SPD}(n).

Usage

SPDMatrix(n, ...)

Arguments

n

An integer value specifying the number of rows and columns of the matrices.
...

Extra arguments to be passed to parent class constructors. See OpenSet and Manifold classes.

Value

An object of class SPDMatrices.

Author(s)

Yann Thanwerdas

See Also

Other symmetric positive definite matrix classes: SPDMatrices

Examples

if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  spd3
}

Class for the Affine Metric on the Manifold of Symmetric Positive Definite Matrices

Description

An R6::R6Class object implementing the SPDMetricAffine class. This is the class for the affine-invariant metric on the SPD manifold (Thanwerdas and Pennec 2019).

Super classes

rgeomstats::PythonClass -> rgeomstats::Connection -> rgeomstats::RiemannianMetric -> SPDMetricAffine

Public fields

n

An integer value specifying the shape of the matrices: n×nn \times n.

power_affine

An integer value specifying the power transformation of the classical SPD metric.

Methods

Public methods

Inherited methods

Method new()

The SPDMetricAffine class constructor.

Usage
SPDMetricAffine$new(n, power_affine = 1, py_cls = NULL)
Arguments
n

An integer value specifying the shape of the matrices: n×nn \times n.

power_affine

An integer value specifying the power transformation of the classical SPD metric. Defaults to 1L.

py_cls

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

Returns

An object of class SPDMetricAffine.

Method clone()

The objects of this class are cloneable with this method.

Usage
SPDMetricAffine$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Author(s)

Yann Thanwerdas

References

Thanwerdas Y, Pennec X (2019). “Is affine-invariance well defined on SPD matrices? A principled continuum of metrics.” In International Conference on Geometric Science of Information, 502–510. Springer.

Class for the Bures-Wasserstein Metric on the Manifold of Symmetric Positive Definite Matrices

Description

An R6::R6Class object implementing the SPDMetricBuresWasserstein class. This is the class for the Bures-Wasserstein metric on the SPD manifold (Bhatia et al. 2019; Malagò et al. 2018).

Super classes

rgeomstats::PythonClass -> rgeomstats::Connection -> rgeomstats::RiemannianMetric -> SPDMetricBuresWasserstein

Public fields

n

An integer value specifying the shape of the matrices: n×nn \times n.

Methods

Public methods

Inherited methods

Method new()

The SPDMetricBuresWasserstein class constructor.

Usage
SPDMetricBuresWasserstein$new(n, py_cls = NULL)
Arguments
n

An integer value specifying the shape of the matrices: n×nn \times n.

py_cls

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

Returns

An object of class SPDMetricBuresWasserstein.

Method clone()

The objects of this class are cloneable with this method.

Usage
SPDMetricBuresWasserstein$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Author(s)

Yann Thanwerdas

References

Bhatia R, Jain T, Lim Y (2019). “On the Bures–Wasserstein distance between positive definite matrices.” Expositiones Mathematicae, 37(2), 165–191.

Malagò L, Montrucchio L, Pistone G (2018). “Wasserstein Riemannian geometry of Gaussian densities.” Information Geometry, 1(2), 137–179.

Class for the Euclidean Metric on the Manifold of Symmetric Positive Definite Matrices

Description

An R6::R6Class object implementing the SPDMetricEuclidean class. This is the class for the Euclidean metric on the SPD manifold.

Super classes

rgeomstats::PythonClass -> rgeomstats::Connection -> rgeomstats::RiemannianMetric -> SPDMetricEuclidean

Public fields

n

An integer value specifying the shape of the matrices: n×nn \times n.

power_euclidean

An integer value specifying the power transformation of the classical SPD metric.

Methods

Public methods

Inherited methods

Method new()

The SPDMetricEuclidean class constructor.

Usage
SPDMetricEuclidean$new(n, power_euclidean = 1, py_cls = NULL)
Arguments
n

An integer value specifying the shape of the matrices: n×nn \times n.

power_euclidean

An integer value specifying the power transformation of the classical SPD metric. Defaults to 1L.

py_cls

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

Returns

An object of class SPDMetricEuclidean.

Method clone()

The objects of this class are cloneable with this method.

Usage
SPDMetricEuclidean$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Author(s)

Yann Thanwerdas

Class for the log-Euclidean Metric on the Manifold of Symmetric Positive Definite Matrices

Description

An R6::R6Class object implementing the SPDMetricLogEuclidean class. This is the class for the log-Euclidean metric on the SPD manifold.

Super classes

rgeomstats::PythonClass -> rgeomstats::Connection -> rgeomstats::RiemannianMetric -> SPDMetricLogEuclidean

Public fields

n

An integer value specifying the shape of the matrices: n×nn \times n.

Methods

Public methods

Inherited methods

Method new()

The SPDMetricLogEuclidean class constructor.

Usage
SPDMetricLogEuclidean$new(n, py_cls = NULL)
Arguments
n

An integer value specifying the shape of the matrices: n×nn \times n.

py_cls

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

Returns

An object of class SPDMetricLogEuclidean.

Examples
if (reticulate::py_module_available("geomstats")) {
  mt <- SPDMetricLogEuclidean$new(n = 3)
  mt
}

Method clone()

The objects of this class are cloneable with this method.

Usage
SPDMetricLogEuclidean$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Author(s)

Yann Thanwerdas

Examples

## ------------------------------------------------
## Method `SPDMetricLogEuclidean$new`
## ------------------------------------------------

if (reticulate::py_module_available("geomstats")) {
  mt <- SPDMetricLogEuclidean$new(n = 3)
  mt
}

Class for the Special Orthogonal Group

Description

This function generates an instance of the class for the special orthogonal group SO(n)\mathrm{SO}(n).

Usage

SpecialOrthogonal(n, point_type = "matrix", epsilon = 0, ..., py_cls = NULL)

Arguments

n

An integer value representing the shape of the ⁠n x n⁠ matrices.
point_type

A character string specifying how elements of the group should be represented. Choices are either "vector" or "matrix". Defaults to "matrix".
epsilon

A numeric value specifying the precision to use for calculations involving potential division by 0 in rotations. Defaults to 0.0.
...

Extra arguments to be passed to parent class constructors. See LieGroup, MatrixLieAlgebra, LevelSet and Manifold classes.
py_cls

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

Value

An object of class SpecialOrthogonal which is an instance of one of three different R6::R6Class depending on the values of the input arguments. Specifically:

  • if n == 2 and point_type == "vector", then the user wants to instantiate the space of 2D rotations in vector representations and thus the output is an instance of the SpecialOrthogonal2Vectors class;

  • if n == 3 and point_type == "vector", then the user wants to instantiate the space of 3D rotations in vector representations and thus the output is an instance of the SpecialOrthogonal3Vectors class;

  • in all other cases, either the user is dealing with rotations in matrix representation or with rotations in dimension greater than 3 and thus the output is an instance of the SpecialOrthogonalMatrices class.

Author(s)

Nicolas Guigui and Nina Miolane

See Also

Other special orthogonal classes: SpecialOrthogonal2Vectors, SpecialOrthogonal3Vectors, SpecialOrthogonalMatrices

Examples

if (reticulate::py_module_available("geomstats")) {
  so3 <- SpecialOrthogonal(n = 3)
  so3
}