Specific manifold functions

This small section extends the functions available from ManifoldsBase.jl and Manifolds.jl, especially a few random generators, that are simpler than the available functions.

reflect(M, p, x)
reflect!(M, q, p, x)

Reflect the point x from the manifold M at point p, i.e.

\[ \operatorname{refl}_p(x) = \exp_p(-\log_p x).\]

where exp and log denote the exponential and logarithmic map on M. This can also be done in place of q.

reflect(M, f, x)
reflect!(M, q, f, x)

reflect the point x from the manifold M at the point f(x) of the function $f: \mathcal M → \mathcal M$, i.e.,

\[ \operatorname{refl}_f(x) = \operatorname{refl}_{f(x)}(x),\]

Compute the result in q.

see also reflect(M,p,x).