Utilities

Ease of notation

The following terms introduce a nicer notation for some operations, for example using the ∈ operator, $p ∈ \mathcal M$ to determine whether $p$ is a point on the AbstractManifold $\mathcal M$.

Base.in — Function

Base.in(p, M::AbstractManifold; kwargs...)
p ∈ M

Check, whether a point p is a valid point (i.e. in) a AbstractManifold M. This method employs is_point deactivating the error throwing option.

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Base.in(p, TpM::TangentSpace; kwargs...)
X ∈ TangentSpace(M, p)

Check whether X is a tangent vector from (in) the tangent space $T_p\mathcal M$, i.e. the TangentSpace at p on the AbstractManifold M. This method uses is_vector deactivating the error throw option.

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Public documentation

Manifolds.sectional_curvature_matrix — Function

sectional_curvature_matrix(M::AbstractManifold, p, B::AbstractBasis)

Compute the matrix of sectional curvatures of manifold M at point p. Entry (i, j) corresponds to sectional curvature of the surface spanned by vectors i and j from basis B.

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