Hi from Italy,
Since our next item on the TensorKitchen.jl to-do list is to add symmetric CP decomposition, we will need a Veronese manifold.
Veronese{𝔽,N,D} <: AbstractManifold{𝔽}
struct Veronese{𝔽,N,D} <: AbstractManifold{𝔽} end
As far as I understand, the Veronese manifold can be viewed as the symmetric, diagonal analogue of the Segre manifold: it corresponds to the rank-one tensor case where all tensor factors are tied together,
$$x_1 = x_2 = \cdots = x_d = x.$$
While working on vector transport for the Segre manifold, I started to understand better how the basic manifold structure and its necessary functions are organized. Thanks to your tutorial on how to create custom manifolds, I would like to suggest implementing a Veronese manifold in Manifolds.jl, although I am still not fully confident about the design.
This would also be useful for TensorKitchen.jl, since symmetric CP decomposition naturally uses rank-one symmetric tensors of the form
$$\left\{
\lambda\, x^{\otimes d}
\;\middle|\;
\lambda \in \mathbb{R}_{>0},\;
x \in \mathbb{S}^{n-1}
\right\}
\subset
(\mathbb{R}^n)^{\otimes d}.$$
Of course, I would work on this with my supervisor’s guidance. I am not completely sure whether adding a general Veronese manifold to Manifolds.jl makes sense from the ecosystem perspective, so I would be very happy to hear your thoughts or suggestions. If you think this should instead be handled differently, I would also completely understand.
Hi from Italy,
Since our next item on the TensorKitchen.jl to-do list is to add symmetric CP decomposition, we will need a Veronese manifold.
Veronese{𝔽,N,D} <: AbstractManifold{𝔽}struct Veronese{𝔽,N,D} <: AbstractManifold{𝔽} endAs far as I understand, the Veronese manifold can be viewed as the symmetric, diagonal analogue of the Segre manifold: it corresponds to the rank-one tensor case where all tensor factors are tied together,
While working on vector transport for the Segre manifold, I started to understand better how the basic manifold structure and its necessary functions are organized. Thanks to your tutorial on how to create custom manifolds, I would like to suggest implementing a
Veronesemanifold in Manifolds.jl, although I am still not fully confident about the design.This would also be useful for TensorKitchen.jl, since symmetric CP decomposition naturally uses rank-one symmetric tensors of the form
Of course, I would work on this with my supervisor’s guidance. I am not completely sure whether adding a general Veronese manifold to Manifolds.jl makes sense from the ecosystem perspective, so I would be very happy to hear your thoughts or suggestions. If you think this should instead be handled differently, I would also completely understand.