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.

Manopt.reflectMethod
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.

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Manopt.reflectMethod
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).

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