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* add spell check GitHub Action
* fix space
* fix a few typos.
* Fix more typos.
* Add a note to contributing.md
---------
Co-authored-by: Ronny Bergmann <git@ronnybergmann.net>
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@@ -17,6 +17,7 @@ The following is a set of guidelines to [`Manopt.jl`](https://juliamanifolds.git
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-[Provide a new example](#Provide-a-new-example)
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-[Code style](#Code-style)
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-[Concerning the documentation](#Concerning-the-documentation)
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-[Spell checking](#Spell-checking)
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## I just have a question
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The developer can most easily be reached in the Julia Slack channel [#manifolds](https://julialang.slack.com/archives/CP4QF0K5Z).
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If you implement a new feature, a tutorial how to use it would be appreciated as well. Tutorials are written as [Quarto](https://quarto.org/) documents and stored in the `tutorials/` folder. This is rendered automatically into the documentation page, you just have to add a menu entry within the tutorial sub menu.
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If you implement an algorithm with a certain numerical example in mind, it would be great, if this could be added to the [ManoptExamples.jl](https://github.com/JuliaManifolds/ManoptExamples.jl) package as well.
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If you implement an algorithm with a certain numerical example in mind, it would be great, if this could be added to the [ManoptExamples.jl](https://github.com/JuliaManifolds/ManoptExamples.jl) package as well.
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### Spell checking
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We use [crate-ci/typos](https://github.com/crate-ci/typos) for spell checking, which is run automatically on GitHub Actions, but you can also run it locally using their command line tool.
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@@ -11,6 +11,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
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### Added
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* a keyword argument `atol` to the `ConstrainedManifoldObjective` to set a tolerance for constraint satisfaction. (#545)
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* a spell checker following [crate-ci/typos](https://github.com/crate-ci/typos)
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### Fixed
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* Removed `atol` from `DebugFeasibility` and instead use the one newly added `atol` from the `ConstrainedManifoldObjective`. (#546)
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* Move from CompatHelper to dependabot to keep track of dependency updates in Julia packages. (#547)
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* moved the `ManoptTestSuite` module to a sub module `Manopt.Test` within `Manopt.jl`,
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so it can be easier resused by others as well (#550)
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so it can be easier reused by others as well (#550)
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* moved to using a `Project.toml` for tests and an overall `[Workspace]`.
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This also allows finally to run single test files without installing all packages manually, but instead just switching to and instantiating the test environment. (#550)
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* for compatibility, state also `[source]` entries consistently in the sub `Project.toml` files. (#550)
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* A scaling error that appeared only when calling `get_cost_function` on the new `ScaledManifoldObjective`.
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* Documentation issues for quasi-Newton solvers.
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* fixes a scaling error in quasi newton
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* Fixes printing of JuMP models containg Manopt solver.
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* Fixes printing of JuMP models containing Manopt solver.
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@@ -41,7 +41,7 @@ The following symbols are used.
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|`:TrustRegionRadius`|[`TrustRegionsState`](@ref)| the trust region radius, equivalent to `:σ`|
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|`:ρ`, `:u`|[`ExactPenaltyCost`](@ref), [`ExactPenaltyGrad`](@ref)| Parameters within the exact penalty objective |
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|`:ρ`, `:μ`, `:λ`|[`AugmentedLagrangianCost`](@ref), [`AugmentedLagrangianGrad`](@ref)| Parameters of the Lagrangian function |
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|`:p`, `:X`|[`LinearizedDCCost`](@ref), [`LinearizedDCGrad`](@ref)| Parameters withing the linearized functional used for the sub problem of the [difference of convex algorithm](@ref solver-difference-of-convex) |
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|`:p`, `:X`|[`LinearizedDCCost`](@ref), [`LinearizedDCGrad`](@ref)| Parameters within the linearized functional used for the sub problem of the [difference of convex algorithm](@ref solver-difference-of-convex) |
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Any other lower case name or letter as well as single upper case letters access fields of the corresponding first argument.
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for example `:p` could be used to access the field `s.p` of a state.
AUTHOR = {Gousenbourger, Pierre-Yves and Massart, Estelle and Musolas, Antoni and Absil, P.-A. and Jacques, Laurent and Hendrickx, Julien M and Marzouk, Youssef},
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# Statement of Need
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In many applications and optimization tasks, non-linear data appears naturally.
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For example, when data on the sphere is measured [@GousenbourgerMassartMusolasAbsilJaquesHendrickxMarzouk:2017], diffusion data can be captured as a signal or even multivariate data of symmetric positive definite matrices [@ValkonenBrediesKnoll2013], and orientations like they appear for electron backscattered diffraction (EBSD) data [@BachmannHielscherSchaeben2011]. Another example are fixed rank matrices, appearing in matrix completion [@Vandereycken:2013:1].
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For example, when data on the sphere is measured [@GousenbourgerMassartMusolasAbsilJacquesHendrickxMarzouk:2017], diffusion data can be captured as a signal or even multivariate data of symmetric positive definite matrices [@ValkonenBrediesKnoll2013], and orientations like they appear for electron backscattered diffraction (EBSD) data [@BachmannHielscherSchaeben2011]. Another example are fixed rank matrices, appearing in matrix completion [@Vandereycken:2013:1].
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Working on these data, for example doing data interpolation and approximation [@BergmannGousenbourger:2018:2], denoising [@LellmannStrekalovskiyKoetterCremers:2013:1; @BergmannFitschenPerschSteidl:2018], inpainting [@BergmannChanHielscherPerschSteidl:2016], or performing matrix completion [@GaoAbsil:2021], can usually be phrased as an optimization problem
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$$ \text{Minimize}\quad f(x) \quad \text{where } x\in\mathcal M, $$
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Given the [`Sphere`](https://juliamanifolds.github.io/Manifolds.jl/v0.7/manifolds/sphere.html) from `Manifolds.jl` and a set of unit vectors $p_1,...,p_N\in\mathbb R^3$, where $N$ is the number of data points,
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we can compute the generalization of the mean, called the Riemannian Center of Mass [@Karcher:1977:1], defined as the minimizer of the squared distances to the given data – a property that the mean in vector spaces fulfills:
where $d_{\mathcal M}$ denotes the length of a shortest geodesic connecting the points specified by its two arguments;
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this is called the Riemannian distance. For the sphere this [`distance`](https://juliamanifolds.github.io/Manifolds.jl/v0.7/manifolds/sphere.html#ManifoldsBase.distance-Tuple{AbstractSphere,%20Any,%20Any}) is given by the length of the shorter great arc connecting the two points.
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