Lorentz Hyperbolic k-Nearest Neighbors

Compute exact k-nearest neighbors under the intrinsic Lorentz hyperbolic distance without returning the full pairwise distance matrix.

Usage

lorentz_knn(Z, k, include_self = FALSE, check = TRUE, tol = 1e-06)

Arguments

Z

An n x 3 matrix of Lorentz hyperboloid points.

k

Number of nearest neighbors to return.

include_self

If TRUE, each row includes itself as the first neighbor with distance zero. If FALSE, self-neighbors are excluded.

check

Logical; validate hyperboloid constraints.

tol

Numerical tolerance.

Value

A list with index, an n x k integer matrix of one-based neighbor indices, distance, an n x k matrix of corresponding hyperbolic distances, k, and include_self.

Examples

H <- simulate_H2(20, r_max = 3)
knn <- lorentz_knn(H$Z, k = 5)
str(knn)