typos

CITATION.bib

@@ -7,7 +7,7 @@ @article{AxenBaranBergmannRzecki:2023
     TITLE      = {Manifolds.jl: An Extensible {J}ulia Framework for Data Analysis on Manifolds},
     YEAR       = {2023}
 }
-@softawre{manifoldsjl-zenodo-mostrecent,
+@software{manifoldsjl-zenodo-mostrecent,
     AUTHOR    = {Seth D. Axen and Mateusz Baran and Ronny Bergmann},
     TITLE     = {Manifolds.jl},
     DOI       = {10.5281/ZENODO.4292129},

NEWS.md

@@ -9,9 +9,13 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Changed
 
-* fixed a few typos in the doc string of the SPD fixed determinant description.
 * Updated `Project.toml` compatibility entries.
 
+### Fixed
+
+* a few typos in the doc string of the SPD fixed determinant description
+* several other typographical errors throughout the documentation
+
 ## [0.9.18] – 2024-05-07
 
 ### Added

_quarto.yml

@@ -1,6 +1,6 @@
 
 project:
-  title: "Manonifolds.jl"
+  title: "Manifolds.jl"
   #execute-dir: project
 
 crossref:

accuracy/Hyperboloid.qmd

@@ -12,7 +12,7 @@ cd(@__DIR__)
 Pkg.activate("."); # for reproducibility use the local accuracy environment.
 ```
 
-In this small note we compare different implementations of several functions on the [Hyperboloic]().
+In this small note we compare different implementations of several functions on the [Hyperbolic]().
 We compare the functions prior [PR #]() to vs those introduced therein.
 We compare the previous version (always called `_1`) and the new version `_2`, where we leave out the manifold to indicate, that these are the local functions here.
 We compare this to the one given in `Manifolds.jl` at time of writing (which is the first one), on `BigFloat` on several scales of magnitudes.
@@ -29,7 +29,7 @@ teal = paul_tol["mutedteal"]
 
 ## Reference Data
 
-We choose a “base point”, a direction and create tangent vectors and correcponding points in several magnutudes of distances
+We choose a “base point”, a direction and create tangent vectors and corresponding points in several magnitudes of distances
 ```{julia}
 #| output: false
 M = Hyperbolic(2)

docs/src/features/atlases.md

@@ -1,6 +1,6 @@
 # [Atlases and charts](@id atlases_and_charts)
 
-Atlases on an ``n``-dimensional manifold ``mathcal M``are collections of charts ``\mathcal A = \{(U_i, φ_i) \colon i \in I\}``, where ``I`` is a (finite or infinte) index family, such that ``U_i \subseteq \mathcal M`` is an open set and each chart ``φ_i: U_i → ℝ^n`` is a homeomorphism. This means, that ``φ_i`` is bijective – sometimes also called one-to-one and onto - and continuous, and its inverse ``φ_i^{-1}`` is continuous as well.
+Atlases on an ``n``-dimensional manifold ``mathcal M``are collections of charts ``\mathcal A = \{(U_i, φ_i) \colon i \in I\}``, where ``I`` is a (finite or infinite) index family, such that ``U_i \subseteq \mathcal M`` is an open set and each chart ``φ_i: U_i → ℝ^n`` is a homeomorphism. This means, that ``φ_i`` is bijective – sometimes also called one-to-one and onto - and continuous, and its inverse ``φ_i^{-1}`` is continuous as well.
 The inverse ``φ_i^{-1}`` is called (local) parametrization.
 The resulting _parameters_ ``a=φ(p)`` of ``p`` (with respect to the chart ``φ``) are in the literature also called “(local) coordinates”. To distinguish the parameter ``a`` from  [`get_coordinates`](@ref) in a basis, we use the terminology parameter in this package.
 

docs/src/manifolds/symmetricpositivedefinite.md

@@ -29,7 +29,7 @@ Pages = ["manifolds/SymmetricPositiveDefiniteAffineInvariant.jl"]
 Order = [:type]
 ```
 
-This metric is also the default metric, i.e. any call of the following functions with `P=SymmetricPositiveDefinite(3)` will result in `MetricManifold(P,AffineInvariantMetric())`and hence yield the formulae described in this seciton.
+This metric is also the default metric, i.e. any call of the following functions with `P=SymmetricPositiveDefinite(3)` will result in `MetricManifold(P,AffineInvariantMetric())`and hence yield the formulae described in this section.
 
 ```@autodocs
 Modules = [Manifolds]

docs/src/misc/notation.md

@@ -59,7 +59,7 @@ Within the documented functions, the utf8 symbols are used whenever possible, as
 | ``e_i \in \mathbb R^n`` | the ``i``th unit vector | ``e_i^n`` | the space dimension (``n``) is omitted, when clear from context
 | ``B`` | a vector bundle | |
 | ``\mathcal T_{q\gets p}X`` | vector transport | | of the vector ``X`` from ``T_p\mathcal M`` to ``T_q\mathcal M``
-| ``\mathcal T_{p,Y}X`` | vector transport in direction ``Y`` | | of the vector ``X`` from ``T_p\mathcal M`` to ``T_q\mathcal M``, where ``q`` is deretmined by ``Y``, for example using the exponential map or some retraction. |
+| ``\mathcal T_{p,Y}X`` | vector transport in direction ``Y`` | | of the vector ``X`` from ``T_p\mathcal M`` to ``T_q\mathcal M``, where ``q`` is determined by ``Y``, for example using the exponential map or some retraction. |
 | ``\operatorname{Vol}(\mathcal M)`` | volume of manifold ``\mathcal M`` | |
 | ``\theta_p(X)`` | volume density for vector ``X`` tangent at point ``p`` | |
 | ``\mathcal W`` | the Weingarten map ``\mathcal W: T_p\mathcal M × N_p\mathcal M → T_p\mathcal M`` | ``\mathcal W_p`` | the second notation to emphasize the dependency of the point ``p\in\mathcal M`` |

docs/src/references.bib

@@ -143,7 +143,7 @@ @article{BergmannGousenbourger:2018
 }
 @book{BinzPods:2008,
     AUTHOR = {Biny, E and Pods, S},
-    PUBLISHER = {American Mathematical Socienty},
+    PUBLISHER = {American Mathematical Society},
     TITLE = {The Geometry of Heisenberg Groups: With Applications in Signal Theory, Optics, Quantization, and Field Quantization},
     YEAR = {2008}
 }

ext/ManifoldsTestExt/tests_general.jl

@@ -63,7 +63,7 @@ that lie on it (contained in `pts`).
 - `test_mutating_rand = false` : test the mutating random function for points on manifolds.
 - `test_project_point = false`: test projections onto the manifold.
 - `test_project_tangent = false` : test projections on tangent spaces.
-- `test_representation_size = true` : test repersentation size of points/tvectprs.
+- `test_representation_size = true` : test representation size of points/tvectprs.
 - `test_tangent_vector_broadcasting = true` : test boradcasting operators on TangentSpace.
 - `test_vector_spaces = true` : test Vector bundle of this manifold.
 - `test_default_vector_transport = false` : test the default vector transport (usually
@@ -841,12 +841,12 @@ function test_manifold(
 end
 
 """
-    test_parallel_transport(M,P; along=false, to=true, diretion=true)
+    test_parallel_transport(M,P; along=false, to=true, direction=true)
 
 Generic tests for parallel transport on `M`given at least two pointsin `P`.
 
 The single functions to transport `along` (a curve), `to` (a point) or (towards a) `direction`
-are sub-tests that can be activated by the keywords arguemnts
+are sub-tests that can be activated by the keywords arguments
 
 !!! Note
 Since the interface to specify curves is not yet provided, the along keyword does not have an effect yet

src/Manifolds.jl

@@ -157,7 +157,7 @@ import ManifoldsBase:
     vector_transport_along,           # just specified in Euclidean - the next 5 as well
     vector_transport_along!,
     vector_transport_along_diff!,     # For consistency these are imported, but for now not
-    vector_transport_along_project!,  # overwritten with new definitons.
+    vector_transport_along_project!,  # overwritten with new definitions.
     vector_transport_direction,
     vector_transport_direction!,
     vector_transport_direction_diff!,
@@ -496,7 +496,7 @@ include("groups/product_group.jl")
 include("groups/semidirect_product_group.jl")
 include("groups/power_group.jl")
 
-# generic group - commopn (special) unitary/orthogonal functions
+# generic group - common (special) unitary/orthogonal functions
 include("groups/general_unitary_groups.jl")
 # Special Group Manifolds
 include("groups/general_linear.jl")

src/groups/general_unitary_groups.jl

@@ -1,7 +1,7 @@
 @doc raw"""
     GeneralUnitaryMultiplicationGroup{T,𝔽,S} <: AbstractDecoratorManifold{𝔽}
 
-A generic type for Lie groups based on a unitary property and matrix multiplcation,
+A generic type for Lie groups based on a unitary property and matrix multiplication,
 see e.g. [`Orthogonal`](@ref), [`SpecialOrthogonal`](@ref), [`Unitary`](@ref), and [`SpecialUnitary`](@ref)
 """
 struct GeneralUnitaryMultiplicationGroup{T,𝔽,S} <: AbstractDecoratorManifold{𝔽}

src/groups/group.jl

@@ -223,7 +223,7 @@ end
 Identity(::O) where {O<:AbstractGroupOperation} = Identity(O)
 Identity(::Type{O}) where {O<:AbstractGroupOperation} = Identity{O}()
 
-# To ensure allocate_result_type works in general if idenitty apears in the tuple
+# To ensure allocate_result_type works in general if identity appears in the tuple
 number_eltype(::Identity) = Bool
 
 @doc raw"""
@@ -431,7 +431,7 @@ end
 Adjoint action of the element `p` of the Lie group `G` on the element `X`
 of the corresponding Lie algebra.
 
-It is defined as the differential of the group authomorphism ``Ψ_p(q) = pqp⁻¹`` at
+It is defined as the differential of the group automorphism ``Ψ_p(q) = pqp⁻¹`` at
 the identity of `G`.
 
 The formula reads
@@ -703,10 +703,10 @@ function hat!(
     return get_vector_lie!(M, Y, X, VeeOrthogonalBasis())
 end
 function hat(M::AbstractManifold, e::Identity, ::Any)
-    return throw(ErrorException("On $M there exsists no identity $e"))
+    return throw(ErrorException("On $M there exists no identity $e"))
 end
 function hat!(M::AbstractManifold, c, e::Identity, X)
-    return throw(ErrorException("On $M there exsists no identity $e"))
+    return throw(ErrorException("On $M there exists no identity $e"))
 end
 
 @trait_function vee(M::AbstractDecoratorManifold, e::Identity, X)
@@ -745,10 +745,10 @@ function vee!(
     return get_coordinates_lie!(M, Y, X, VeeOrthogonalBasis())
 end
 function vee(M::AbstractManifold, e::Identity, X)
-    return throw(ErrorException("On $M there exsists no identity $e"))
+    return throw(ErrorException("On $M there exists no identity $e"))
 end
 function vee!(M::AbstractManifold, c, e::Identity, X)
-    return throw(ErrorException("On $M there exsists no identity $e"))
+    return throw(ErrorException("On $M there exists no identity $e"))
 end
 
 """
@@ -1245,7 +1245,7 @@ end
 @doc raw"""
     get_vector_lie(G::AbstractDecoratorManifold, a, B::AbstractBasis)
 
-Reconstruct a tangent vector from the Lie algebra of `G` from cooordinates `a` of a basis `B`.
+Reconstruct a tangent vector from the Lie algebra of `G` from coordinates `a` of a basis `B`.
 This is similar to calling [`get_vector`](@ref) at the `p=`[`Identity`](@ref)`(G)`.
 """
 function get_vector_lie(

src/groups/product_group.jl

@@ -65,7 +65,7 @@ end
 
 function is_identity(G::ProductGroup, p::Identity{<:ProductOperation}; kwargs...)
     pes = submanifold_components(G, p)
-    M = G.manifold # Inner prodct manifold (of groups)
+    M = G.manifold # Inner product manifold (of groups)
     return all(map((M, pe) -> is_identity(M, pe; kwargs...), M.manifolds, pes))
 end
 

src/manifolds/Circle.jl

@@ -354,7 +354,7 @@ manifold_volume(::Circle) = 2 * π
     mean(M::Circle{ℝ}, x::AbstractVector[, w::AbstractWeights])
 
 Compute the Riemannian [`mean`](@ref mean(M::AbstractManifold, args...)) of `x` of points on
-the [`Circle`](@ref) ``𝕊^1``, reprsented by real numbers, i.e. the angular mean
+the [`Circle`](@ref) ``𝕊^1``, represented by real numbers, i.e. the angular mean
 ````math
 \operatorname{atan}\Bigl( \sum_{i=1}^n w_i\sin(x_i),  \sum_{i=1}^n w_i\sin(x_i) \Bigr).
 ````
@@ -375,7 +375,7 @@ end
     mean(M::Circle{ℂ}, x::AbstractVector[, w::AbstractWeights])
 
 Compute the Riemannian [`mean`](@ref mean(M::AbstractManifold, args...)) of `x` of points on
-the [`Circle`](@ref) ``𝕊^1``, reprsented by complex numbers, i.e. embedded in the complex plane.
+the [`Circle`](@ref) ``𝕊^1``, represented by complex numbers, i.e. embedded in the complex plane.
 Comuting the sum
 ````math
 s = \sum_{i=1}^n x_i
@@ -510,7 +510,7 @@ sym_rem(x, T=π) = map(sym_rem, x, Ref(T))
 Compute the parallel transport of `X` from the tangent space at `p` to the tangent space at
 `q` on the [`Circle`](@ref) `M`.
 For the real-valued case this results in the identity.
-For the complex-valud case, the formula is the same as for the [`Sphere`](@ref)`(1)` in the
+For the complex-valued case, the formula is the same as for the [`Sphere`](@ref)`(1)` in the
 complex plane.
 ````math
 \mathcal P_{q←p} X = X - \frac{⟨\log_p q,X⟩_p}{d^2_{ℂ}(p,q)}

src/manifolds/Elliptope.jl

@@ -56,7 +56,7 @@ end
 @doc raw"""
     check_point(M::Elliptope, q; kwargs...)
 
-checks, whether `q` is a valid reprsentation of a point ``p=qq^{\mathrm{T}}`` on the
+checks, whether `q` is a valid representation of a point ``p=qq^{\mathrm{T}}`` on the
 [`Elliptope`](@ref) `M`, i.e. is a matrix
 of size `(N,K)`, such that ``p`` is symmetric positive semidefinite and has unit trace.
 Since by construction ``p`` is symmetric, this is not explicitly checked.

src/manifolds/EmbeddedTorus.jl

@@ -34,7 +34,7 @@ Check whether `p` is a valid point on the [`EmbeddedTorus`](@ref) `M`.
 The tolerance for the last test can be set using the `kwargs...`.
 
 The method checks if ``(p_1^2 + p_2^2 + p_3^2 + R^2 - r^2)^2``
-is apprximately equal to ``4R^2(p_1^2 + p_2^2)``.
+is approximately equal to ``4R^2(p_1^2 + p_2^2)``.
 """
 function check_point(M::EmbeddedTorus, p; kwargs...)
     A = (dot(p, p) + M.R^2 - M.r^2)^2

src/manifolds/Euclidean.jl

@@ -659,23 +659,23 @@ end
 """
     parallel_transport_along(M::Euclidean, p, X, c)
 
-the parallel transport on [`Euclidean`](@ref) is the identiy, i.e. returns `X`.
+the parallel transport on [`Euclidean`](@ref) is the identity, i.e. returns `X`.
 """
 parallel_transport_along(::Euclidean, ::Any, X, c::AbstractVector) = X
 parallel_transport_along!(::Euclidean, Y, ::Any, X, c::AbstractVector) = copyto!(Y, X)
 
 """
     parallel_transport_direction(M::Euclidean, p, X, d)
 
-the parallel transport on [`Euclidean`](@ref) is the identiy, i.e. returns `X`.
+the parallel transport on [`Euclidean`](@ref) is the identity, i.e. returns `X`.
 """
 parallel_transport_direction(::Euclidean, ::Any, X, ::Any) = X
 parallel_transport_direction!(::Euclidean, Y, ::Any, X, ::Any) = copyto!(Y, X)
 
 """
     parallel_transport_to(M::Euclidean, p, X, q)
 
-the parallel transport on [`Euclidean`](@ref) is the identiy, i.e. returns `X`.
+the parallel transport on [`Euclidean`](@ref) is the identity, i.e. returns `X`.
 """
 parallel_transport_to(::Euclidean, ::Any, X, ::Any) = X
 parallel_transport_to!(::Euclidean, Y, ::Any, X, ::Any) = copyto!(Y, X)

src/manifolds/GeneralizedGrassmann.jl

@@ -99,7 +99,7 @@ end
     check_point(M::GeneralizedGrassmann, p)
 
 Check whether `p` is representing a point on the [`GeneralizedGrassmann`](@ref) `M`, i.e. its
-a `n`-by-`k` matrix of unitary column vectors with respect to the B inner prudct and
+a `n`-by-`k` matrix of unitary column vectors with respect to the B inner product and
 of correct `eltype` with respect to `𝔽`.
 """
 function check_point(M::GeneralizedGrassmann, p; kwargs...)
@@ -359,7 +359,7 @@ end
 @doc raw"""
     representation_size(M::GeneralizedGrassmann)
 
-Return the represenation size or matrix dimension of a point on the [`GeneralizedGrassmann`](@ref)
+Return the representation size or matrix dimension of a point on the [`GeneralizedGrassmann`](@ref)
 `M`, i.e. ``(n,k)`` for both the real-valued and the complex value case.
 """
 representation_size(M::GeneralizedGrassmann) = get_parameter(M.size)

src/manifolds/Hamiltonian.jl

@@ -78,7 +78,7 @@ end
 ManifoldsBase.@default_manifold_fallbacks HamiltonianMatrices Hamiltonian Hamiltonian value value
 
 @doc raw"""
-    ^(A::Hamilonian, ::typeof(+))
+    ^(A::Hamiltonian, ::typeof(+))
 
 Compute the [`symplectic_inverse`](@ref) of a Hamiltonian (A)
 """

src/manifolds/Hyperbolic.jl

@@ -24,7 +24,7 @@ metric. The corresponding sectional curvature is ``-1``.
 If `p` and `X` are `Vector`s of length `n+1` they are assumed to be
 a [`HyperboloidPoint`](@ref) and a [`HyperboloidTVector`](@ref), respectively
 
-Other models are the Poincaré ball model, see [`PoincareBallPoint`](@ref) and [`PoincareBallTVector`](@ref), respectiely
+Other models are the Poincaré ball model, see [`PoincareBallPoint`](@ref) and [`PoincareBallTVector`](@ref), respectively
 and the Poincaré half space model, see [`PoincareHalfSpacePoint`](@ref) and [`PoincareHalfSpaceTVector`](@ref), respectively.
 
 # Constructor
@@ -52,7 +52,7 @@ end
 In the Hyperboloid model of the [`Hyperbolic`](@ref) ``\mathcal H^n`` points are represented
 as vectors in ``ℝ^{n+1}`` with [`MinkowskiMetric`](@ref) equal to ``-1``.
 
-This representation is the default, i.e. `AbstractVector`s are assumed to have this repesentation.
+This representation is the default, i.e. `AbstractVector`s are assumed to have this representation.
 """
 struct HyperboloidPoint{TValue<:AbstractVector} <: AbstractManifoldPoint
     value::TValue
@@ -65,7 +65,7 @@ In the Hyperboloid model of the [`Hyperbolic`](@ref) ``\mathcal H^n`` tangent vc
 as vectors in ``ℝ^{n+1}`` with [`MinkowskiMetric`](@ref) ``⟨p,X⟩_{\mathrm{M}}=0`` to their base
 point ``p``.
 
-This representation is the default, i.e. vectors are assumed to have this repesentation.
+This representation is the default, i.e. vectors are assumed to have this representation.
 """
 struct HyperboloidTVector{TValue<:AbstractVector} <: TVector
     value::TValue
@@ -148,7 +148,7 @@ For the [`HyperboloidPoint`](@ref) or plain vectors this means that, `p` is a ve
 length ``n+1`` with inner product in the embedding of -1, see [`MinkowskiMetric`](@ref).
 The tolerance for the last test can be set using the `kwargs...`.
 
-For the [`PoincareBallPoint`](@ref) a valid point is a vector ``p ∈ ℝ^n`` with a norm stricly
+For the [`PoincareBallPoint`](@ref) a valid point is a vector ``p ∈ ℝ^n`` with a norm strictly
 less than 1.
 
 For the [`PoincareHalfSpacePoint`](@ref) a valid point is a vector from ``p ∈ ℝ^n`` with a positive
@@ -288,7 +288,7 @@ reaches `q` after time 1. The formula reads for ``p ≠ q``
 ```
 
 where ``⟨⋅,⋅⟩_{\mathrm{M}}`` denotes the [`MinkowskiMetric`](@ref) on the embedding,
-the [`Lorentz`](@ref)ian manifold. For ``p=q`` the logarihmic map is equal to the zero vector.
+the [`Lorentz`](@ref)ian manifold. For ``p=q`` the logarithmic map is equal to the zero vector.
 """
 log(::Hyperbolic, ::Any...)
 
@@ -368,7 +368,7 @@ end
 @doc raw"""
     parallel_transport_to(M::Hyperbolic, p, X, q)
 
-Compute the paralllel transport of the `X` from the tangent space at `p` on the
+Compute the parallel transport of the `X` from the tangent space at `p` on the
 [`Hyperbolic`](@ref) space ``\mathcal H^n`` to the tangent at `q` along the [`geodesic`](@extref `ManifoldsBase.geodesic-Tuple{AbstractManifold, Any, Any}`)
 connecting `p` and `q`. The formula reads
 

src/manifolds/HyperbolicPoincareBall.jl

@@ -303,7 +303,7 @@ end
 @doc raw"""
     project(::Hyperbolic, ::PoincareBallPoint, ::PoincareBallTVector)
 
-projction of tangent vectors in the Poincaré ball model is just the identity, since
+projection of tangent vectors in the Poincaré ball model is just the identity, since
 the tangent space consists of all ``ℝ^n``.
 """
 project(::Hyperbolic, ::PoincareBallPoint, ::PoincareBallTVector)

src/manifolds/HyperbolicPoincareHalfspace.jl

@@ -253,7 +253,7 @@ end
 @doc raw"""
     project(::Hyperbolic, ::PoincareHalfSpacePoint ::PoincareHalfSpaceTVector)
 
-projction of tangent vectors in the Poincaré half space model is just the identity, since
+projection of tangent vectors in the Poincaré half space model is just the identity, since
 the tangent space consists of all $ℝ^n$.
 """
 project(::Hyperbolic, ::PoincareHalfSpacePoint::PoincareHalfSpaceTVector)

src/manifolds/Hyperrectangle.jl

@@ -321,15 +321,15 @@ LinearAlgebra.norm(::Hyperrectangle, ::Any, X) = norm(X)
 """
     parallel_transport_direction(M::Hyperrectangle, p, X, d)
 
-the parallel transport on [`Hyperrectangle`](@ref) is the identiy, i.e. returns `X`.
+the parallel transport on [`Hyperrectangle`](@ref) is the identity, i.e. returns `X`.
 """
 parallel_transport_direction(::Hyperrectangle, ::Any, X, ::Any) = X
 parallel_transport_direction!(::Hyperrectangle, Y, ::Any, X, ::Any) = copyto!(Y, X)
 
 """
     parallel_transport_to(M::Hyperrectangle, p, X, q)
 
-the parallel transport on [`Hyperrectangle`](@ref) is the identiy, i.e. returns `X`.
+the parallel transport on [`Hyperrectangle`](@ref) is the identity, i.e. returns `X`.
 """
 parallel_transport_to(::Hyperrectangle, ::Any, X, ::Any) = X
 parallel_transport_to!(::Hyperrectangle, Y, ::Any, X, ::Any) = copyto!(Y, X)