Package index • manifoldtest

Distance covariance independence test for manifold-valued data.

manifold.dcov.test(): Distance covariance independence test for manifold-valued data.

Definition and retrieval of the manifolds supported by the package.

Manifold-agnostic choice of the base point of the logarithmic map.

Geometry of the flat torus, with points represented in [0,1)^d.

is_in_torus(): Check that data lies in the torus representation [0,1)^d.
log_map_torus(): Map torus data to the tangent space at a base point.
dist_torus(): Torus distance from a data set to a point.
is_valid_torus(): Check whether a base point is valid for a torus data set.
auto_base_point_torus(): Find a torus base point via the maximal-gap method.
optimize_base_point_torus(): Find a torus base point via multi-start optimization.
largest_gap_point_torus(): Midpoint of the largest gap on the circle [0,1).

Geometry of the hyperbolic space in the hyperboloid model.

is_in_hyperbolic(): Check that data lies on the hyperboloid.
log_map_hyperbolic(): Map hyperbolic data to the tangent space at a base point.
exp_map_hyperbolic(): Map tangent vectors to hyperbolic space.
dist_hyperbolic(): Hyperbolic distance from a data set to a point.
is_valid_hyperbolic(): Check whether a base point is valid for a hyperbolic data set.
auto_base_point_hyperbolic(): Find a hyperbolic base point via the Lorentzian centroid.
optimize_base_point_hyperbolic(): Find a hyperbolic base point via multi-start optimization.

Geometry of the Grassmann manifold Gr(n, k), with points represented by Stiefel matrices.

is_in_grassmann(): Check that data lies on the Grassmann manifold.
log_map_grassmann(): Map Grassmann data to the tangent space at a base point.
exp_map_grassmann(): Map tangent vectors to the Grassmann manifold.
dist_grassmann(): Grassmann distance from a data set to a point.
is_valid_grassmann(): Check whether a base point is valid for a Grassmann data set.
auto_base_point_grassmann(): Find a Grassmann base point via the projection mean.
optimize_base_point_grassmann(): Find a Grassmann base point via multi-start optimization.

Multidimensional ranks in the unit ball (Hallin et al. 2021).

center_outward_transform(): Center-outward transform.
build_ball_grid(): Build a regular grid on the unit ball.
optimal_assignment(): Solve the optimal L2 assignment between data and grid.

Helper functions for data preparation.