
# The adjoint differential of the exponential map base point

This function evaluates for $F(x)=\exp_x\xi$ with fixed $\xi\in T_x\M$ the adjoint differenital $D^*_xF(x)[\eta].$

It is calculated a corresponding adjoint Jacobi field AdjJacoiField. Since the weights are the same as for the differential DxExp, we refer to that page for details.

### Matlab Documentation

1
2
3
4
5
6
7
8
9
10
11
%   nu = AdjDxExp(x,xi,eta) - Adjoint of the Derivative of Exp with
%   respect to the basis point
%    INPUT
%      x   : base point of the exponential
%      xi  : direction of the exponential
%     eta  : (in TExp(x,xi)M) direction to take the Adjoint derivative at.
%
%    OUTPUT
%     nu   : ( in TxM ) - the adjoint of DxExp with respect to eta
% ---
% MVIRT R. Bergmann, 2017-12-04