Map tangent vectors to hyperbolic space.

Exponential map of \(H^d\) at base point p, the inverse of log_map_hyperbolic. Useful to simulate data on \(H^d\).

Usage

exp_map_hyperbolic(V, p = c(1, rep(0, ncol(V))))

Arguments

V

Numeric matrix with d columns: tangent-space coordinates at p, one row per point.

p

Numeric vector of length d + 1: the base point on the hyperboloid. Defaults to \((1, 0, \ldots, 0)\).

Value

A numeric matrix with nrow(V) rows and d + 1 columns: points on the hyperboloid.

Examples

X <- exp_map_hyperbolic(matrix(rnorm(20), nrow = 10, ncol = 2))
is_in_hyperbolic(X)
#> [1] TRUE