Define Meta Manifolds already in ManifoldsBase

.github/workflows/ci.yml

@@ -11,11 +11,8 @@ jobs:
     runs-on: ${{ matrix.os }}
     strategy:
       matrix:
-        julia-version: ["1.0", "1.6", "1.9"]
+        julia-version: ["1.6", "1.9", "~1.10.0-0"]
         os: [ubuntu-latest, macOS-latest, windows-latest]
-        exclude:
-          - os: macOS-latest
-            julia-version: "1.0"
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1

NEWS.md

@@ -5,11 +5,37 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [0.15.0] xx/xx/2023
+
+### Added
+
+- `ProductManifold` type was migrated from Manifolds.jl.
+- `Fiber`, `VectorSpaceFiber` and `TangentSpace` types. `TangentSpace` is a generalized version of `TangentSpaceAtPoint` from Manifolds.jl.
+- `change_representer!`, `change_metric!` and `Weingarten!` methods added to `PowerManifold`.
+- `×` now also works for retractions, inverse retractions, and vector transports to create their product versions
+- `retract`, `inverse_retract`, and `vector_transport_to` (and `_dir`) now also accept arbirtrary retractions on the product manifold. These act the same as the n-fold product of a retraction.
+
+### Changed
+
+- `Requires.jl` is added as a dependency to facilitate loading some methods related to `ProductManifolds` on Julia 1.6 to 1.8. Later versions rely on package extensions.
+- `Documenter.jl` was updated to 1.0.
+- `PowerManifold` can now store its size either in a field or in a type, similarly to `DefaultManifold`. By default the size is stored in a field.
+
+### Removed
+
+- Julia 1.0 is no longer supported. From now on, the earliest supported Julia version is 1.6.
+
+## [0.14.12] 23/09/2023
+
+### Changed
+
+- Introduce a thorough way to allocate tangent vectors for `rand`
+
 ## [0.14.11] 25/08/2023
 
 ### Added
 
-- MAke the `Weingarten` map a decorator capable function.
+- Make the `Weingarten` map a decorator capable function.
 
 ## [0.14.10] 17/08/2023
 

Project.toml

@@ -1,24 +1,34 @@
 name = "ManifoldsBase"
 uuid = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
 authors = ["Seth Axen <[email protected]>", "Mateusz Baran <[email protected]>", "Ronny Bergmann <[email protected]>", "Antoine Levitt <[email protected]>"]
-version = "0.14.12"
+version = "0.15.0"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+
+[weakdeps]
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+
+[extensions]
+ManifoldsBaseRecursiveArrayToolsExt = "RecursiveArrayTools"
 
 [compat]
 DoubleFloats = ">= 0.9.2"
+RecursiveArrayTools = "2"
+Requires = "1"
 julia = "1.0"
 
 [extras]
 DoubleFloats = "497a8b3b-efae-58df-a0af-a86822472b78"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "DoubleFloats", "ForwardDiff", "OrdinaryDiffEq", "ReverseDiff", "StaticArrays"]
+test = ["Test", "DoubleFloats", "ForwardDiff", "OrdinaryDiffEq", "ReverseDiff", "StaticArrays", "RecursiveArrayTools"]

docs/Project.toml

@@ -1,9 +1,11 @@
 [deps]
 CondaPkg = "992eb4ea-22a4-4c89-a5bb-47a3300528ab"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244"
 ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
 
 [compat]
 CondaPkg = "0.2"
-Documenter = "0.27"
-ManifoldsBase = "0.14"
+Documenter = "1"
+DocumenterCitations = "1.2"
+ManifoldsBase = "0.15"

docs/make.jl

@@ -30,9 +30,13 @@ if "--quarto" ∈ ARGS
 end
 
 using Documenter: DocMeta, HTML, MathJax3, deploydocs, makedocs
+using DocumenterCitations
 using ManifoldsBase
 
-makedocs(
+# (e) ...finally! make docs
+bib = CitationBibliography(joinpath(@__DIR__, "src", "references.bib"); style = :alpha)
+makedocs(;
+    # for development, we disable prettyurls
     format = HTML(;
         mathengine = MathJax3(),
         prettyurls = get(ENV, "CI", nothing) == "true",
@@ -53,8 +57,11 @@ makedocs(
             "Vector transports" => "vector_transports.md",
         ],
         "Manifolds" => "manifolds.md",
+        "Meta-Manifolds" => "metamanifolds.md",
         "Decorating/Extending a Manifold" => "decorator.md",
         "Bases for tangent spaces" => "bases.md",
+        "References" => "references.md",
     ],
+    plugins = [bib],
 )
 deploydocs(repo = "github.com/JuliaManifolds/ManifoldsBase.jl.git", push_preview = true)

docs/src/assets/citations.css

@@ -0,0 +1,19 @@
+/* Taken from https://juliadocs.org/DocumenterCitations.jl/v1.2/styling/ */
+
+.citation dl {
+  display: grid;
+  grid-template-columns: max-content auto; }
+.citation dt {
+  grid-column-start: 1; }
+.citation dd {
+  grid-column-start: 2;
+  margin-bottom: 0.75em; }
+.citation ul {
+ padding: 0 0 2.25em 0;
+ margin: 0;
+ list-style: none;}
+.citation ul li {
+ text-indent: -2.25em;
+ margin: 0.33em 0.5em 0.5em 2.25em;}
+.citation ol li {
+ padding-left:0.75em;}

docs/src/manifolds.md

@@ -3,29 +3,7 @@
 While the interface `ManifoldsBase.jl` does not cover concrete manifolds, it provides a few
 helpers to build or create manifolds based on existing manifolds
 
-## [(Abstract) power manifold](@id sec-power-manifold)
-
-A power manifold is constructed like higher dimensional vector spaces are formed from the real line, just that for every point ``p = (p_1,\ldots,p_n) ∈ \mathcal M^n`` on the power manifold ``\mathcal M^n`` the entries of ``p`` are points ``p_1,\ldots,p_n ∈ \mathcal M`` on some manifold ``\mathcal M``. Note that ``n`` can also be replaced by multiple values, such that ``p`` is not a vector but a matrix or a multi-index array of points.
-
-```@autodocs
-Modules = [ManifoldsBase]
-Pages = ["src/PowerManifold.jl"]
-Order = [:macro, :type, :function]
-```
-
-## `ValidationManifold`
-
-[`ValidationManifold`](@ref) is a simple decorator using the [`AbstractDecoratorManifold`](@ref) that “decorates” a manifold with tests that all involved points and vectors are valid for the wrapped manifold.
-For example involved input and output paratemers are checked before and after running a function, repectively.
-This is done by calling [`is_point`](@ref) or [`is_vector`](@ref) whenever applicable.
-
-```@autodocs
-Modules = [ManifoldsBase]
-Pages = ["ValidationManifold.jl"]
-Order = [:macro, :type, :function]
-```
-
-## `DefaultManifold`
+## A default manifold
 
 [`DefaultManifold`](@ref ManifoldsBase.DefaultManifold) is a simplified version of [`Euclidean`](https://juliamanifolds.github.io/Manifolds.jl/latest/manifolds/euclidean.html) and demonstrates a basic interface implementation.
 It can be used to perform simple tests.
@@ -71,3 +49,16 @@ Modules = [ManifoldsBase]
 Pages = ["metric.jl"]
 Order = [:type, :function]
 ```
+
+
+## A manifold for validation
+
+[`ValidationManifold`](@ref) is a simple decorator using the [`AbstractDecoratorManifold`](@ref) that “decorates” a manifold with tests that all involved points and vectors are valid for the wrapped manifold.
+For example involved input and output paratemers are checked before and after running a function, repectively.
+This is done by calling [`is_point`](@ref) or [`is_vector`](@ref) whenever applicable.
+
+```@autodocs
+Modules = [ManifoldsBase]
+Pages = ["ValidationManifold.jl"]
+Order = [:macro, :type, :function]
+```

docs/src/metamanifolds.md

@@ -0,0 +1,37 @@
+# Meta Manifolds
+
+While the interface does not provide concrete manifolds itself, it does provide several manifolds that can be build based on a given [`AbstractManifold`](@ref) instance.
+
+## [(Abstract) power manifold](@id sec-power-manifold)
+
+A power manifold is constructed like higher dimensional vector spaces are formed from the real line, just that for every point ``p = (p_1,\ldots,p_n) ∈ \mathcal M^n`` on the power manifold ``\mathcal M^n`` the entries of ``p`` are points ``p_1,\ldots,p_n ∈ \mathcal M`` on some manifold ``\mathcal M``. Note that ``n`` can also be replaced by multiple values, such that ``p`` is not a vector but a matrix or a multi-index array of points.
+
+```@autodocs
+Modules = [ManifoldsBase]
+Pages = ["src/PowerManifold.jl"]
+Order = [:macro, :type, :function]
+```
+
+## [Product Manifold](@id ProductManifold)
+
+```@autodocs
+Modules = [ManifoldsBase]
+Pages = ["src/ProductManifold.jl"]
+Order = [:macro, :type, :function]
+```
+
+## Fiber
+
+```@autodocs
+Modules = [ManifoldsBase]
+Pages = ["Fiber.jl"]
+Order = [:macro, :type, :function]
+```
+
+## Tangent Space
+
+```@autodocs
+Modules = [ManifoldsBase]
+Pages = ["TangentSpace.jl"]
+Order = [:macro, :type, :function]
+```

docs/src/references.bib

@@ -0,0 +1,87 @@
+# ManifoldBase.jl
+#
+# Literature used within the Documentation of ManifoldsBase.jl
+# ========================================================
+#
+# citekeys should be of the form AllAuthors:Year, unless there is really many authors.
+#
+# ----------------------------------------------------------------------------------------
+@book{AbsilMahonySepulchre:2008,
+    AUTHOR    = {Absil, P.-A. and Mahony, R. and Sepulchre, R.},
+    DOI       = {10.1515/9781400830244},
+    NOTE      = {available online at [press.princeton.edu/chapters/absil/](http://press.princeton.edu/chapters/absil/)},
+    PUBLISHER = {Princeton University Press},
+    TITLE     = {Optimization Algorithms on Matrix Manifolds},
+    YEAR      = {2008},
+}
+
+@article{EhlersPiraniSchild:1972,
+    DOI       = {10.1007/s10714-012-1353-4},
+    YEAR      = {1972},
+    PUBLISHER = {Springer Science and Business Media {LLC}},
+    VOLUME    = {44},
+    NUMBER    = {6},
+    PAGES     = {1587--1609},
+    AUTHOR    = {J\"{u}rgen Ehlers and Felix A. E. Pirani and Alfred Schild},
+    TITLE     = {Republication of: The geometry of free fall and light propagation},
+    JOURNAL   = {General Relativity and Gravitation}
+}
+
+@article{LorenziPennec:2013,
+    DOI        = {10.1007/s10851-013-0470-3},
+    EPRINT     = {00870489},
+    EPRINTTYPE = {HAL},
+    YEAR       = {2013},
+    VOLUME     = {50},
+    NUMBER     = {1-2},
+    PAGES      = {5--17},
+    AUTHOR     = {Marco Lorenzi and Xavier Pennec},
+    TITLE      = {Efficient Parallel Transport of Deformations in Time Series of Images: From Schild's to Pole Ladder},
+    JOURNAL    = {Journal of Mathematical Imaging and Vision}
+}
+@book{Lee:2019,
+    AUTHOR = {John M. Lee},
+    DOI    = {10.1007/978-3-319-91755-9},
+    ISBN = {978-3-319-91755-9},
+    PUBLISHER = {Springer Cham},
+    TITLE  = {Introduction to Riemannian Manifolds},
+    YEAR   = {2019}
+}
+@inproceedings{MuralidharanFletcher:2012,
+    DOI       = {10.1109/cvpr.2012.6247780},
+    YEAR      = 2012,
+    AUTHOR    = {P. Muralidharan and P. T. Fletcher},
+    TITLE     = {Sasaki metrics for analysis of longitudinal data on manifolds},
+    BOOKTITLE = {2012 {IEEE} Conference on Computer Vision and Pattern Recognition}
+}
+@article{Pennec:2018,
+    AUTHOR ={Xavier Pennec},
+    EPRINT = {1805.11436},
+    EPRINTTYPE = {arXiv},
+    Journal = {arXiv Preprint},
+    TITLE = {Parallel Transport with Pole Ladder: a Third Order Scheme in Affine Connection Spaces which is Exact in Affine Symmetric Spaces.},
+    YEAR = {2018},
+    URL = {https://arxiv.org/abs/1805.11436},
+}
+@article{Sasaki:1958,
+    DOI     = {10.2748/tmj/1178244668},
+    YEAR    = {1958},
+    VOLUME  = {10},
+    NUMBER  = {3},
+    AUTHOR  = {Shigeo Sasaki},
+    TITLE   = {On the differential geometry of tangent bundles of Riemannian manifolds},
+    JOURNAL = {Tohoku Math. J.}
+}
+@article{SatoIwai:2013,
+    AUTHOR        = {Hiroyuki Sato and Toshihiro Iwai},
+    ARCHIVEPREFIX = {arXiv},
+    DOI           = {10.1080/02331934.2013.836650},
+    EPRINT        = {1302.0125},
+    JOURNAL       = {Optimization},
+    NUMBER        = {4},
+    PAGES         = {1011--1031},
+    PUBLISHER     = {Informa {UK} Limited},
+    TITLE         = {A new,  globally convergent Riemannian conjugate gradient method},
+    VOLUME        = {64},
+    YEAR          = {2013}
+}

docs/src/references.md

@@ -0,0 +1,4 @@
+# Literature
+
+```@bibliography
+```

docs/src/types.md

@@ -9,7 +9,12 @@ Throughout the documentation of `ManifoldsBase.jl` we might use the [Euclidean S
 AbstractManifold
 ```
 
-which should store information about the manifold, for example parameters inherent to the manifold.
+which should store information about the manifold, for example parameters inherent to the manifold. The parameters are stored in two possible ways, as a type parameter to dispatch on or as a field. For these the following internal functions exist
+
+```@docs
+ManifoldsBase.wrap_type_parameter
+ManifoldsBase.TypeParameter
+```
 
 ## Points on a manifold
 

docs/src/vector_transports.md

@@ -7,7 +7,7 @@ A _vector transport_ is a way to transport a vector between two tangent spaces.
 Let ``p,q ∈ \mathcal M`` be given, ``c`` the curve along which we want to transport (cf. [parallel transport](@ref subsec-parallel-transport), for example a geodesic or curve given by a retraction.
 We can specify the geodesic or curve a retraction realises for example by a direction ``d``.
 
-More precisely using [^AbsilMahonySepulchre2008], Def. 8.1.1, a vector transport
+More precisely using [AbsilMahonySepulchre:2008](@cite), Def. 8.1.1, a vector transport
 ``T_{p,d}: T_p\mathcal M \to T_q\mathcal M``, ``p∈ \mathcal M``, ``Y∈ T_p\mathcal M`` is a smooth mapping
 associated to a retraction ``\operatorname{retr}_p(Y) = q`` such that