Manifold {rgeomstats}R Documentation

Abstract Class for Manifolds

Description

An R6::R6Class object implementing the base Manifold class. In other words, a topological space that locally resembles Euclidean space near each point.

Super class

rgeomstats::PythonClass -> Manifold

Public fields

dim

An integer value specifying the dimension of the manifold.

shape

An integer vector specifying the shape of one element of the manifold. Defaults to NULL.

metric

A RiemannianMetric object specifying the metric to use on the manifold. Defaults to NULL.

default_coords_type

A string specifying the coordinate type. Choices are extrensic or intrinsic. Dedaults to intrinsic.

default_point_type

A string specifying the point type. Choices are vector or matrix. It is automatically determined depending on the manifold.

Methods

Public methods

Inherited methods

Method new()

The Manifold class constructor.

Usage
Manifold$new(
  dim,
  shape = NULL,
  metric = NULL,
  default_coords_type = "intrinsic",
  py_cls = NULL
)
Arguments
dim

An integer value specifying the dimension of the manifold.

shape

An integer vector specifying the shape of one element of the manifold. Defaults to NULL.

metric

A RiemannianMetric object specifying the metric to use on the manifold. Defaults to NULL.

default_coords_type

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

py_cls

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

Returns

An object of class Manifold.

Method belongs()

Evaluates if a point belongs to the manifold.

Usage
Manifold$belongs(point, atol = gs$backend$atol)
Arguments
point

A numeric array of shape [\dots \times \{\mathrm{dim}\}] specifying one or more points to be checked.

atol

A numeric value specifying the absolute tolerance for checking. Defaults to gs$backend$atol.

Returns

A boolean value or vector storing whether the corresponding points belong to the manifold.

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

Method is_tangent()

Checks whether a vector is tangent at a base point.

Usage
Manifold$is_tangent(vector, base_point = NULL, atol = gs$backend$atol)
Arguments
vector

A numeric array of shape [\dots \times [\mathrm{dim}]] specifying one or more vectors to be checked.

base_point

A numeric array of shape [\dots \times [\mathrm{dim}]] specifying one or more base points on the manifold. Defaults to NULL in which case the identity is used.

atol

A numeric value specifying the absolute tolerance for checking. Defaults to gs$backend$atol.

Returns

A boolean value or vector storing whether the corresponding points are tangent to the manifold at corresponding base points.

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

Method to_tangent()

Projects a vector to a tangent space of the manifold.

Usage
Manifold$to_tangent(vector, base_point = NULL)
Arguments
vector

A numeric array of shape [\dots \times [\mathrm{dim}]] specifying one or more vectors to project on the manifold.

base_point

A numeric array of shape [\dots \times [\mathrm{dim}]] specifying one or more base points on the manifold. Defaults to NULL in which case the identity is used.

Returns

A numeric array of shape [\dots \times \{\mathrm{dim}\}] storing the corresponding projections onto the manifold at corresponding base points.

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

Method random_point()

Samples random points on the manifold.

Usage
Manifold$random_point(n_samples = 1, bound = 1)
Arguments
n_samples

An integer value specifying the number of samples to be drawn. Defaults to 1L.

bound

A numeric value specifying the bound of the interval in which to sample for non-compact manifolds. Defaults to 1L.

Details

If the manifold is compact, a uniform distribution is used.

Returns

A numeric array of shape [\dots \times \{\mathrm{dim}\}] storing a sample of points on the manifold.

Examples
if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  # spd3$random_point(10) # TO DO: uncomment when bug fixed in gs
}

Method regularize()

Regularizes a point to the canonical representation for the manifold.

Usage
Manifold$regularize(point)
Arguments
point

A numeric array of shape [\dots \times [\mathrm{dim}]] specifying one or more points on the manifold.

Returns

A numeric array of the same shape storing the corresponding regularized points.

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

Method set_metric()

Sets the Riemannian Metric associated to the manifold.

Usage
Manifold$set_metric(metric)
Arguments
metric

An object of class RiemannianMetric.

Returns

The Manifold class itself invisibly.

Examples
if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  spd3$metric
  spd3$set_metric(SPDMetricBuresWasserstein$new(n = 3))
  spd3$metric
}

Method random_tangent_vec()

Generates a random tangent vector.

Usage
Manifold$random_tangent_vec(base_point, n_samples = 1)
Arguments
base_point

A numeric array of shape [\dots \times \{\mathrm{dim}\}] specifying one or more base points on the manifold.

n_samples

An integer value specifying the number of samples to be drawn. Defaults to 1L.

Returns

A numeric array of shape [\dots \times \{\mathrm{dim}\}] storing a sample of vectors that are tangent to the manifold at corresponding base points.

Examples
if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  spd3$random_tangent_vec(diag(1, 3), 10)
}

Method clone()

The objects of this class are cloneable with this method.

Usage
Manifold$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Author(s)

Nina Miolane

Examples


## ------------------------------------------------
## Method `Manifold$belongs`
## ------------------------------------------------

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

## ------------------------------------------------
## Method `Manifold$is_tangent`
## ------------------------------------------------

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

## ------------------------------------------------
## Method `Manifold$to_tangent`
## ------------------------------------------------

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

## ------------------------------------------------
## Method `Manifold$random_point`
## ------------------------------------------------

if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  # spd3$random_point(10) # TO DO: uncomment when bug fixed in gs
}

## ------------------------------------------------
## Method `Manifold$regularize`
## ------------------------------------------------

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

## ------------------------------------------------
## Method `Manifold$set_metric`
## ------------------------------------------------

if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  spd3$metric
  spd3$set_metric(SPDMetricBuresWasserstein$new(n = 3))
  spd3$metric
}

## ------------------------------------------------
## Method `Manifold$random_tangent_vec`
## ------------------------------------------------

if (reticulate::py_module_available("geomstats")) {
  spd3 <- SPDMatrix(n = 3)
  spd3$random_tangent_vec(diag(1, 3), 10)
}
[Package rgeomstats version 0.0.1 Index]