
# The inner product for cyclic data

The tangent vectors on $\mathbb S^1$ lie on a line (when looking at the embedded circle), and hence the dot prodcut is the product of the tangent vectors, which are here values.

### Matlab Documentation

1
2
3
4
5
6
7
8
9
10
11
12
13
14
% S1.dot(x,xi,nu)
%     Compute the inner product of two tangent vectors in T_P M
%
% INPUT
%     x  : a point(Set) in S1
%     xi  : a first tangent vector( set) to (each) x
%     nu  : a secod tangent vector( set) to (each) x
%
% OUTPUT
%     ds : the corresponding value(s) of the inner product of (each triple) V,W at X
%
% ---
% Manifold-Valued Image Restoration Toolbox 1.0, J. Persch 2016-12-06
%