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Tangent-Space Coordinates

Source: R/tangent.R
tangent_coordinates.Rd

Map Lorentz hyperboloid points to two-dimensional coordinates in a Lorentz-orthonormal basis of T_mu H^2.

Usage

tangent_coordinates(Z, mu = NULL)

Arguments

Z

n x 3 Lorentz hyperboloid coordinates.

mu

Reference point. If NULL, the normalized extrinsic mean is used.

Value

An n x 2 matrix of tangent coordinates.

Details

The columns express lorentz_log_map() in an orthonormal tangent basis. Their ordinary Euclidean norm equals the Lorentz norm of the tangent vector. This routine uses the log map's default zero-distance threshold 1e-10. To compare training and new points, pass the same mu in both calls; separately estimated centers define different coordinate systems.

Examples

H <- simulate_H2(5, r_max = 2)
tangent_coordinates(H$Z)