Class for the Affine Metric on the Manifold of Symmetric Positive Definite Matrices
Source:R/spd-metric-affine.R
SPDMetricAffine.RdAn R6::R6Class object implementing the SPDMetricAffine
class. This is the class for the affine-invariant metric on the SPD
manifold (Thanwerdas and Pennec 2019)
.
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.
Super classes
rgeomstats::PythonClass -> rgeomstats::Connection -> rgeomstats::RiemannianMetric -> SPDMetricAffine
Public fields
nAn integer value specifying the shape of the matrices: \(n \times n\).
power_affineAn integer value specifying the power transformation of the classical SPD metric.
Methods
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
nAn integer value specifying the shape of the matrices: \(n \times n\).
power_affineAn integer value specifying the power transformation of the classical SPD metric. Defaults to
1L.py_clsA Python object of class
SPDMetricAffine. Defaults toNULLin which case it is instantiated on the fly using the other input arguments.