Merge branch 'kellertuer/general-linear-group' of github.com:JuliaMan…

…ifolds/LieGroups.jl into kellertuer/general-linear-group

docs/src/tutorials/transition.md

@@ -35,7 +35,7 @@ The list is alphabetical, but first lists types, then functions
 | `exp(G, g, X)` | `exp(`[`base_manifold`](@ref base_manifold(G::LieGroup))`(G), g, X)` | the previous defaults whenever not agreeing with the invariant one can now be accessed on the internal manifold |
 | `exp_inv(G, g, X)` | [`exp`](@ref exp(G::LieGroup, g, X, t::Number))`(G, g, X)`  | the exponential map invariant to the group operation is the default on Lie groups here |
 | `exp_lie(G, X)` | [`exp`](@ref exp(G::LieGroup, e::Identity, X, t::Number))`(G, `[`Identity`](@ref)`(G), X)` | the (matrix) exponential is now the one at the [`Identity`](@ref)`(G)`, since there it agrees with the invariant one |
-| `invervse_translate(G, g, h, c)` | [`inv_left_compose`](@ref)`(G, g, h)`, [`inv_right_compose`](@ref)`(G, g, h)` | compute ``g^{-1}∘h`` and ``g∘h^{-1}``, resp. |
+| `inverse_translate(G, g, h, c)` | [`inv_left_compose`](@ref)`(G, g, h)`, [`inv_right_compose`](@ref)`(G, g, h)` | compute ``g^{-1}∘h`` and ``g∘h^{-1}``, resp. |
 | `inverse_tranlsate_diff(G, g, h, X, LeftForwardAction())` | - | discontinued, use `diff_left_compose(G, inv(G,g), h)` |
 | `inverse_tranlsate_diff(G, g, h, X, RightBackwardAction())` | - | discontinued, use `diff_left_compose(G, h, inv(G,g))` |
 | `log(G, g, h)` | `log(`[`base_manifold`](@ref base_manifold(G::LieGroup))`(G), g, h)` | you can now access the previous defaults on the internal manifold whenever they do not agree with the invariant one |

src/group_operations/multiplication_operation.jl

@@ -10,7 +10,7 @@ abstract type AbstractMultiplicationGroupOperation <: AbstractGroupOperation end
 """
     AbstractMultiplicationGroupOperation <: AbstractMultiplicationGroupOperation
 
-A grou poperation that is realised by a matrix multiplication.
+A group operation that is realised by a matrix multiplication.
 """
 struct MatrixMultiplicationGroupOperation <: AbstractMultiplicationGroupOperation end
 
@@ -309,7 +309,7 @@ Base.log(
     g,
 ) where {𝔽} = log(g)
 
-@doc "$(_doc_exp_mult)"
+@doc "$(_doc_log_mult)"
 function ManifoldsBase.log!(
     ::LieGroup{𝔽,MatrixMultiplicationGroupOperation},
     X,

src/groups/general_linear_group.jl

@@ -24,9 +24,9 @@ const GeneralLinearGroup{𝔽,T} = LieGroup{
     𝔽,MatrixMultiplicationGroupOperation,Manifolds.InvertibleMatrices{𝔽,T}
 }
 
-function GeneralLinearGroup(n::Int...; kwargs...)
-    Im = Manifolds.InvertibleMatrices(n...; kwargs...)
-    return GeneralLinearGroup{typeof(Im).parameters[[1, 2]]...}(
+function GeneralLinearGroup(n::Int; kwargs...)
+    Im = Manifolds.InvertibleMatrices(n; kwargs...)
+    return GeneralLinearGroup{typeof(Im).parameters...}(
         Im, MatrixMultiplicationGroupOperation()
     )
 end

src/interface.jl

@@ -399,7 +399,7 @@ _doc_get_coordinates = """
 Return the vector of coordinates to the decomposition of `X` with respect to an [`AbstractBasis`](@extref `ManifoldsBase.AbstractBasis`)
 of the [`LieAlgebra`](@ref) `𝔤`.
 Since all tangent vectors are assumed to be represented in the Lie algebra,
-both signatures are equivalend.
+both signatures are equivalent.
 The operation can be performed in-place of `c`.
 
 By default this function requires [`identity_element`](@ref)`(G)` and calls
@@ -449,7 +449,7 @@ _doc_hat = """
     hat!(G::LieGroup, X, c)
 
 Compute the hat map ``(⋅)^̂ `` that maps a vector of coordinates ``c_i``
-with respect to a certain basis to an tangent vector in the Lie algebra
+with respect to a certain basis to a tangent vector in the Lie algebra
 
 ```math
 X = $(_tex(:sum))_{i∈$(_tex(:Cal,"I"))} c_iB_i,
@@ -602,7 +602,7 @@ end
 Check whether `g` is a valid point on the Lie Group `G`.
 This falls back to checking whether `g` is a valid point on `G.manifold`,
 unless `g` is an [`Identity`](@ref). Then, it is checked whether it is the
-idenity element corresponding to `G`.
+identity element corresponding to `G`.
 """
 ManifoldsBase.is_point(G::LieGroup, g; kwargs...)
 
@@ -720,10 +720,10 @@ end
 LinearAlgebra.norm(G::LieGroup, g, X) = norm(G.manifold, g, X)
 
 _doc_rand = """
-    rand(::LieGroup; vector_at=nothing, σ=1.0, kwargs...)
-    rand(::LieAlgebra; σ=1.0, kwargs...)
-    rand!(::LieGroup, gX; vector_at=nothing, kwargs...)
-    rand!(::LieAlgebra, X; σ=1.0, kwargs...)
+    rand(::LieGroup; vector_at=nothing, σ::Real=1.0, kwargs...)
+    rand(::LieAlgebra; σ::Real=1.0, kwargs...)
+    rand!(::LieGroup, gX; vector_at=nothing, σ::Real=1.0, kwargs...)
+    rand!(::LieAlgebra, X; σ::Real=1.0, kwargs...)
 
 Compute a random point or tangent vector on a Lie group.