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

An R6::R6Class object implementing the SPDMetricAffine class. This is the class for the affine-invariant metric on the SPD manifold thanwerdas2019affinergeomstats.

References

Author

Yann Thanwerdas

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.