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Remove Grassmann, since it was the wrong representation.
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kellertuer committed Aug 18, 2023
1 parent 46ec946 commit 4583dc4
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23 changes: 0 additions & 23 deletions src/manifolds/GrassmannStiefel.jl
Original file line number Diff line number Diff line change
Expand Up @@ -356,29 +356,6 @@ projecting it onto the tangent space at q.
"""
vector_transport_to(::Grassmann, ::Any, ::Any, ::Any, ::ProjectionTransport)

@doc raw"""
Weingarten(M::Grassmann, p, X, V)
Compute the Weingarten map ``\mathcal W_p`` at `p` on the [`Grassmann`](@ref) `M` with
respect to the tangent vector ``X \in T_p\mathcal M`` and the normal vector ``V \in N_p\mathcal M``.
The formula is due to [AbsilMahonyTrumpf:2013](@cite) given by
```math
\mathcal W_p(X,V) = -\operatorname{ad}_p\bigl(\operatorname{ad}_V(X),
```
where $\operatorname{ad}_pX := [p,X] := pX - Xp$.
"""
Weingarten(::Grassmann, p, X, V)

_ad(p, X) = p * X - X * p

function Weingarten!(::Grassmann, Y, p, X, V)
Y .= -_ad(p, _ad(V, X))
return Y
end

@doc raw"""
zero_vector(M::Grassmann, p)
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2 changes: 1 addition & 1 deletion src/manifolds/Stiefel.jl
Original file line number Diff line number Diff line change
Expand Up @@ -346,7 +346,7 @@ Compute the retraction on the [`Stiefel`](@ref) that is based on the Cayley tran
Using
````math
W_{p,X} = \operatorname{P}_pXp^{\mathrm{H}} - pX^{\mathrm{H}}\operatorname{P_p}
\quad\text{where}
\quad\text{where}
\operatorname{P}_p = I - \frac{1}{2}pp^{\mathrm{H}}
````
the formula reads
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6 changes: 3 additions & 3 deletions src/manifolds/StiefelEuclideanMetric.jl
Original file line number Diff line number Diff line change
Expand Up @@ -136,8 +136,8 @@ end
project(M::Stiefel,p)
Projects `p` from the embedding onto the [`Stiefel`](@ref) `M`, i.e. compute `q`
as the polar decomposition of $p$ such that $q^{\mathrm{H}q$ is the identity,
where $\cdot^{\mathrm{H}}$ denotes the hermitian, i.e. complex conjugate transposed.
as the polar decomposition of $p$ such that ``q^{\mathrm{H}}q`` is the identity,
where ``\cdot^{\mathrm{H}}`` denotes the hermitian, i.e. complex conjugate transposed.
"""
project(::Stiefel, ::Any, ::Any)

Expand All @@ -154,7 +154,7 @@ Project `X` onto the tangent space of `p` to the [`Stiefel`](@ref) manifold `M`.
The formula reads
````math
\operatorname{proj}_{\mathcal M}(p, X) = X - p \operatorname{Sym}(p^{\mathrm{H}}X),
\operatorname{proj}_{T_p\mathcal M}(X) = X - p \operatorname{Sym}(p^{\mathrm{H}}X),
````
where $\operatorname{Sym}(q)$ is the symmetrization of $q$, e.g. by
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