GeodRegr (version 0.2.0)

geo_dist: Geodesic distance between two points on a manifold

Description

Finds the Riemannian distance \(d(p_1,p_2)=||\textrm{Log}_{p_1}(p_2)||\) between two points on the given manifold, provided \(p_2\) is in the domain of \(\textrm{Log}_{p_1}\).

Usage

geo_dist(manifold, p1, p2)

Arguments

manifold

Type of manifold ('euclidean', 'sphere', 'hyperbolic', or 'kendall').

p1

A vector (or column matrix) representing a point on the manifold.

p2

A vector (or column matrix) representing a point on the manifold.

Value

Riemannian distance between p1 and p2.

Details

On the sphere, \(-p_1\) is not in the domain of \(\textrm{Log}_{p_1}\).

See Also

log_map.

Examples

# NOT RUN {
p1 <- matrix(rnorm(10), ncol = 2)
p1 <- p1[, 1] + (1i) * p1[, 2]
p1 <- (p1 - mean(p1)) / norm(p1 - mean(p1), type = '2')
p2 <- matrix(rnorm(10), ncol = 2)
p2 <- p2[, 1] + (1i) * p2[, 2]
p2 <- (p2 - mean(p2)) / norm(p2 - mean(p2), type = '2')
geo_dist('kendall', p1, p2)

# }