SPDMetricAffine {rgeomstats}

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 \times n.

power_affine

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

Methods

Public methods

• SPDMetricAffine$new()

• SPDMetricAffine$clone()

Inherited methods

• rgeomstats::PythonClass$get_python_class()
• rgeomstats::PythonClass$set_python_class()
• rgeomstats::Connection$christoffels()
• rgeomstats::Connection$curvature()
• rgeomstats::Connection$curvature_derivative()
• rgeomstats::Connection$directional_curvature()
• rgeomstats::Connection$directional_curvature_derivative()
• rgeomstats::Connection$exp()
• rgeomstats::Connection$geodesic()
• rgeomstats::Connection$geodesic_equation()
• rgeomstats::Connection$injectivity_radius()
• rgeomstats::Connection$ladder_parallel_transport()
• rgeomstats::Connection$log()
• rgeomstats::Connection$parallel_transport()
• rgeomstats::RiemannianMetric$closest_neighbor_index()
• rgeomstats::RiemannianMetric$cometric_matrix()
• rgeomstats::RiemannianMetric$diameter()
• rgeomstats::RiemannianMetric$dist()
• rgeomstats::RiemannianMetric$dist_broadcast()
• rgeomstats::RiemannianMetric$dist_pairwise()
• rgeomstats::RiemannianMetric$hamiltonian()
• rgeomstats::RiemannianMetric$inner_coproduct()
• rgeomstats::RiemannianMetric$inner_product()
• rgeomstats::RiemannianMetric$inner_product_derivative_matrix()
• rgeomstats::RiemannianMetric$metric_matrix()
• rgeomstats::RiemannianMetric$norm()
• rgeomstats::RiemannianMetric$normal_basis()
• rgeomstats::RiemannianMetric$normalize()
• rgeomstats::RiemannianMetric$random_unit_tangent_vec()
• rgeomstats::RiemannianMetric$sectional_curvature()
• rgeomstats::RiemannianMetric$squared_dist()
• rgeomstats::RiemannianMetric$squared_norm()

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 \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.