📚

.gitignore

@@ -5,3 +5,4 @@ docs/src/generated
 docs/src/misc/contributing.md
 benchmark/tune.json
 benchmark/results*
+docs/src/tutorials/*.md

docs/Project.toml

@@ -6,7 +6,9 @@ Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 HybridArrays = "1baab800-613f-4b0a-84e4-9cd3431bfbb9"
 Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
+MarkdownLiteral = "736d6165-7244-6769-4267-6b50796e6954"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PlutoStaticHTML = "359b1769-a58e-495b-9770-312e911026ad"
 PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

docs/make.jl

@@ -1,4 +1,5 @@
 using Plots, RecipesBase, Manifolds, ManifoldsBase, Documenter, PyPlot
+using PlutoStaticHTML
 # required for loading the manifold tests functios
 using Test, FiniteDifferences
 ENV["GKSwstype"] = "100"
@@ -23,6 +24,41 @@ open(joinpath(generated_path, "contributing.md"), "w") do io
     end
 end
 
+#
+# Generate Pluto Tutorial HTMLs
+tutorial_menu = Array{Pair{String,String},1}()
+tutorial_src_folder = joinpath(@__DIR__, "..", "tutorials/")
+tutorial_output_folder = joinpath(@__DIR__, "src/", "tutorials/")
+tutorial_relative_path = "tutorials/"
+mkpath(tutorial_output_folder)
+#
+# Tutorials
+@info " \n      Rendering Tutorials\n "
+tutorials = [Dict(:file => "getstarted", :title => "Get started with Manifolds.jl")]
+# build menu and write files myself - tp set edit url correctly.
+for t in tutorials
+    global tutorial_menu
+    rendered = build_notebooks( #though not really parallel here
+        BuildOptions(
+            tutorial_src_folder;
+            output_format=documenter_output,
+            write_files=false,
+            use_distributed=false,
+        ),
+        ["$(t[:file]).jl"],
+    )
+    write(
+        tutorial_output_folder * t[:file] * ".md",
+        """
+        ```@meta
+        EditURL = "$(tutorial_src_folder)$(t[:file]).jl"
+        ```
+        $(rendered["$(t[:file]).jl"][1])
+        """,
+    )
+    push!(tutorial_menu, t[:title] => joinpath(tutorial_relative_path, t[:file] * ".md"))
+end
+
 makedocs(
     # for development, we disable prettyurls
     format=Documenter.HTML(prettyurls=false, assets=["assets/favicon.ico"]),
@@ -31,6 +67,7 @@ makedocs(
     sitename="Manifolds.jl",
     pages=[
         "Home" => "index.md",
+        "Tutorials" => tutorial_menu,
         "Manifolds" => [
             "Basic manifolds" => [
                 "Centered matrices" => "manifolds/centeredmatrices.md",

src/manifolds/FixedRankMatrices.jl

@@ -84,9 +84,11 @@ Base.:(==)(x::SVDMPoint, y::SVDMPoint) = (x.U == y.U) && (x.S == y.S) && (x.Vt =
 @doc raw"""
     UMVTVector <: TVector
 
-A tangent vector that can be described as a product `U_p M V_p^\mathrm{H} + U_X V_p^\mathrm{H} + U_p V_X^\mathrm{H}`,
-where `X = U_X S V_X^\mathrm{H}` is its base point, see for example [`FixedRankMatrices`](@ref).
-This vector structure stores the additionally (to the point) required fields.
+A tangent vector that can be described as a product ``U_p M V_p^\mathrm{H} + U_X V_p^\mathrm{H} + U_p V_X^\mathrm{H}```,
+where ``X = U_X S V_X^\mathrm{H}`` is its base point, see for example [`FixedRankMatrices`](@ref).
+
+The base point ``p`` is required for example embedding this point, but it is not stored.
+The fields of thie tangent vector are `U` for ``U_X``, `M` and `Vt` to store ``V_X^\mathrm{H}``
 
 # Constructors
 * `UMVTVector(U,M,Vt)` store umv factors to initialize the `UMVTVector`

src/manifolds/VectorBundle.jl

@@ -85,7 +85,7 @@ TangentSpaceAtPoint(M::AbstractManifold, p) = VectorSpaceAtPoint(TangentBundleFi
 """
     TangentSpace(M::AbstractManifold, p)
 
-Return a [`TangentSpaceAtPoint`](@ref TangentSpaceAtPoint{AbstractManifold, Any}) representing tangent space at `p` on the [`AbstractManifold`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/types.html#ManifoldsBase.AbstractManifold) `M`.
+Return a [`TangentSpaceAtPoint`](@ref) representing tangent space at `p` on the [`AbstractManifold`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/types.html#ManifoldsBase.AbstractManifold) `M`.
 """
 TangentSpace(M::AbstractManifold, p) = VectorSpaceAtPoint(TangentBundleFibers(M), p)
 
@@ -603,7 +603,7 @@ end
 @doc raw"""
     injectivity_radius(M::TangentSpaceAtPoint)
 
-Return the injectivity radius on the [`TangentSpaceAtPoint`](@ref) `M`, which is $∞$.
+Return the injectivity radius on the [`TangentSpaceAtPoint`](@ref TangentSpaceAtPoint) `M`, which is $∞$.
 """
 injectivity_radius(::TangentSpaceAtPoint) = Inf