exp_map {GeodRegr}

Exponential map

Description

Performs the exponential map \textrm{Exp}_p(v) on the given manifold.

Usage

exp_map(manifold, p, v)

Arguments

manifold

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

p

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

v

A vector (or column matrix) tangent to p.

Value

A vector representing a point on the manifold.

Author(s)

Ha-Young Shin

References

Fletcher, P. T. (2013). Geodesic regression and the theory of least squares on Riemannian manifolds. International Journal of Computer Vision, 105, 171-185.

Cornea, E., Zhu, H., Kim, P. and Ibrahim, J. G. (2017). Regression models on Riemannian symmetric spaces. Journal of the Royal Statistical Society: Series B, 79, 463-482.

Calinon, S. (2020). Gaussians on Riemannian manifolds: Applications for robot learning and adaptive control. IEEE Robotics & Automation Magazine, 27, 33-45.

Shin, H.-Y. and Oh H.-S. (2020). Robust Geodesic Regression. <arXiv:2007.04518>

See Also

log_map.

Examples

exp_map('hyperbolic', c(1, 0, 0, 0, 0), c(0, 0, pi / 4, 0, 0))