Adress points from code review.

src/manifolds/CenteredMatrices.jl

@@ -119,7 +119,7 @@ where $c_i = \frac{1}{m}\sum_{j=1}^m x_{j,i}$  for $i = 1, \dots, n$.
 """
 project(::CenteredMatrices, ::Any, ::Any)
 
-project!(::CenteredMatrices, Y, p::Any, X) = (Y .= X .- mean(X, dims=1))
+project!(::CenteredMatrices, Y, p, X) = (Y .= X .- mean(X, dims=1))
 
 @generated representation_size(::CenteredMatrices{m,n,𝔽}) where {m,n,𝔽} = (m, n)
 

src/manifolds/HyperbolicPoincareBall.jl

@@ -11,9 +11,7 @@ function change_gradient(
     X::PoincareBallTVector,
 )
     α = 2 / (1 - norm(p.value)^2)
-    Y = copy(M, p, X)
-    Y.value ./= α^2
-    return Y
+    return PoincareBallTVector(X.value ./ α^2)
 end
 
 @doc raw"""
@@ -29,9 +27,7 @@ function change_metric(
     X::PoincareBallTVector,
 )
     α = 2 / (1 - norm(p.value)^2)
-    Y = copy(M, p, X)
-    Y.value ./= α
-    return Y
+    return PoincareBallTVector(X.value ./ α)
 end
 
 function check_point(M::Hyperbolic{N}, p::PoincareBallPoint; kwargs...) where {N}

src/manifolds/MetricManifold.jl

@@ -95,7 +95,7 @@ Here, the default metric in `\mathcal P(3)` is the [`LinearAffineMetric`](@ref)
 """
 change_gradient(::AbstractManifold, ::AbstractMetric, ::Any, ::Any)
 
-function change_tangent(M::AbstractManifold, G::AbstractMetric, p, X)
+function change_gradient(M::AbstractManifold, G::AbstractMetric, p, X)
     if is_default_metric(M, G)
         return X
     end
@@ -108,7 +108,7 @@ function change_tangent(M::AbstractManifold, G::AbstractMetric, p, X)
     return get_vector(M, p, z, B)
 end
 
-function change_metric(
+function change_gradient(
     ::MetricManifold{𝔽,M,G},
     ::G,
     p,
@@ -128,8 +128,6 @@ sense that it returns the tangent vector ``Z=BX`` such that the linear map ``B``
 g_2(Y_1,Y_2) = g_1(BY_1,BY_2) \quad \text{for all } Y_1, Y_2 ∈ T_p\mathcal M.
 ````
 
-holds.
-
 If both metrics are given in their [`local_metric`](@ref) (symmetric positive defintie) matrix
 representations ``G_1 = C_1C_1^{\mathrm{H}}`` and ``G_2 = C_2C_2^{\mathrm{H}}``, where ``C_1,C_2`` denote their
 Cholesky factor, then solving ``C_2C_2^{\mathrm{H}} = G_2 = B^{\mathrm{H}}G_1B = B^{\mathrm{H}}C_1C_1^{\mathrm{H}}B`` yields ``B = (C_1 \backslash C_2)^{\mathrm{H}}``,
@@ -234,7 +232,7 @@ Return the [`LeviCivitaConnection`](@ref) for a metric manifold.
 connection(::MetricManifold) = LeviCivitaConnection()
 
 @doc raw"""
-    det_local_metric(M::AbstractManifold, p, B::AbstractBasis=DefaultOrthogonalBasis)
+    det_local_metric(M::AbstractManifold, p, B::AbstractBasis)
 
 Return the determinant of local matrix representation of the metric tensor ``g``, i.e. of the
 matrix ``G(p)`` representing the metric in the tangent space at ``p`` with as a matrix.

src/manifolds/PositiveNumbers.jl

@@ -58,15 +58,15 @@ end
 
 Given a tangent vector ``X ∈ T_p\mathcal M``representing a gradient with respect to the [`EuclideanMetric`](@ref) `g_E`,
 this function changes into the positivity metric representation of
-[`PositiveNumbers`](lref) `M` for the same gradient.
+[`PositiveNumbers`](@ref) `M` for the same gradient.
 """
 change_gradient(::PositiveNumbers, ::EuclideanMetric, p, X) = p .* X .* p
 
 @doc raw"""
     change_metric(M::SymmetricPOsitiveDefinite, E::EuclideanMetric, p, X)
 
 Given a tangent vector ``X ∈ T_p\mathcal M`` with respect to the [`EuclideanMetric`](@ref) `g_E`,
-this function changes into the positivity metric of [`PositiveNumbers`](lref) `M` for the same gradient.
+this function changes into the positivity metric of [`PositiveNumbers`](@ref) `M` for the same gradient.
 """
 change_metric(::PositiveNumbers, ::EuclideanMetric, p, X) = p .* X
 

src/manifolds/PowerManifold.jl

@@ -95,7 +95,7 @@ end
 
 Since the metric on a power manifold decouples, the change of a representer can be done elementwise
 """
-function change_gradient(::AbstractPowerManifold, M::AbstractMetric, p, X)
+function change_metric(::AbstractPowerManifold, M::AbstractMetric, p, X)
     Z = copy(M, p, X)
     for i in get_iterator(M)
         Z[i...] = change_gradient(M.manifold, G, p[i...], X[i...])

src/manifolds/SymmetricPositiveDefiniteLinearAffine.jl

@@ -11,7 +11,7 @@ struct LinearAffineMetric <: RiemannianMetric end
 
 Given a tangent vector ``X ∈ T_p\mathcal M``representing a gradient with respect to the [`EuclideanMetric`](@ref) `g_E`,
 this function changes into the [`LinearAffine`](@ref) (default) metric representation of
-[`SymmetricPOsitiveDefinite`](lref) `M` for the same gradient.
+[`SymmetricPOsitiveDefinite`](@ref) `M` for the same gradient.
 """
 change_gradient(::SymmetricPositiveDefinite, ::EuclideanMetric, p, X) = p * X * p
 
@@ -20,7 +20,7 @@ change_gradient(::SymmetricPositiveDefinite, ::EuclideanMetric, p, X) = p * X *
 
 Given a tangent vector ``X ∈ T_p\mathcal M`` with respect to the [`EuclideanMetric`](@ref) `g_E`,
 this function changes into the [`LinearAffine`](@ref) (default) metric on the
-[`SymmetricPOsitiveDefinite`](lref) `M`.
+[`SymmetricPOsitiveDefinite`](@ref) `M`.
 """
 change_metric(::SymmetricPositiveDefinite, ::EuclideanMetric, p, X) = p * X