implementation the complex counterpart of real manifold factory

[longfei.ga...@gmail.com]

Many engineering problem appears with complex arguments. 

It is indeed possible to convert the complex formulation into its real counterpart. 

However, it is convenient to directly deal with the complex formulation.

 

I think it would be nice to add some complex counterpart of real manifold factory to Manopt. More researchers will benefit from it. 

List some complex manifold as follows:

complex oblique 

complex elliptope 

complex spectrahedron

Hermitte positive definite matrices

Above complex manifolds appear frequently in beamforming vector or covariance matrix design problems. 

[BM]

Hello, 

Thanks for the interest in Manopt and the suggestions. 

As you have rightly pointed out, the complex manifold geometries would be useful in many applications. Adding more of them to Manopt is certainly also our goal. We are also keen on contributions from fellow researchers who have expertise in complex manifolds.

Regards,

Bamdev