Seth Axen

I guess it depends what you mean by "random". For a compact embedded manifold, the easiest way will be to sample with a multivariate normal in the ambient space and...

> For a general Riemannian manifold, the usual "uniform" measure is the area/volume/Hausdorf measure, but for Lie groups, "uniform" probably best corresponds to the Haar measure. There was a discussion...

And one more note, in order to have `logpdf` implementations, we'll definitely want `Uniform` distributions to be their own type. e.g. if the uniform distribution can be implemented as a...

After further thought, I think it makes more sense to explicitly have `Hausdorff` and `Haar{

It maybe should be moved to ManifoldMeasures.jl, which is carrying out the plan discussed here, but given how experimental that package is and that it itself could be discontinued, I'd...

I also think `ManifoldsBase.jl` is a good idea and should definitely include `Euclidean`. > I think issues 1-3 should be solved before `Manifolds.jl` can be safely used in `Optim.jl` (or...

Yeah, I think even just a simple splash page with a logo for each package we consider usable would be useful.

Perhaps, though which packages would we consider usable right now? Manifolds.jl, ManifoldsBase.jl, and ManOpt.jl for sure. Is FunManifolds.jl usable? I think it would be premature to create logos for packages...

> The gradient is always a tangent vector; the differential always yields a cotangent. My differential geometry is not good, but isn't the gradient in fact a cotangent vector?

I may tackle this in the coming weeks as I want to use `mean` on the `Stiefel` manifold.