
# The logarithmic map on the hyperbolic space

The logarithmic map on the sphere $\mathbb H^n$ is defined for any $x,y\in\mathbb S^n$ by

where $\langle\cdot,\cdot\rangle_M$ denotes the Minkowski metric.

### Matlab Documentation

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% xi = log(x,y) logarithmic map the point(s) x from y
%
% INPUT
%   x : a point or set of points on the manifold Hn
%   y : a point or set of points on the manifold Hn
%
% OUTPUT
%   xi : resulting point(s) of x(i) to y(i) elementwise
%
% ---
% Manifold-Valued Image Restoration Toolbox 1.1
% R. Bergmann ~ 2015-10-20