A Tutorial when starting with a new manifold

[kellertuer]

This is an approach to resolve #305.

Maybe it is also a good idea on this PR to first have a few more “Technical Details” pages per solver similar to https://manoptjl.org/stable/solvers/gradient_descent.html#Technical-Details.

• finished a new tutorial
• introduce vale.sh to reduce errors and formatting in docs – though for now just in md files not yet in doc strings.
• add “Technical Details” sections to other solvers
  • ARC solver
  • alternating gradient descent
  • ALM
  • Chambolle–Pock
  • CG
  • DoC
  • DouglasRachford
  • EPM
  • gradient descent
  • Levenbeg–Marquardt
  • Nelder–Mead
  • particle swarm
  • primal dual semi smooth Newton
  • quasi Newton
  • SGD
  • tCG
  • trust regions

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (c1fc4a5) 99.74% compared to head (77d8768) 99.74%.

Additional details and impacted files

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  Coverage   99.74%   99.74%           
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  Files          79       79           
  Lines        7353     7353           
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  Hits         7334     7334           
  Misses         19       19           

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[kellertuer]

@blegat before continuing with more technical details sections (they take a bit of time not to miss a function) – can you check whether a tutorial like https://manoptjl.org/previews/PR314/tutorials/ImplementOwnManifold.html is what you would have liked to have?

[blegat]

Yes, it's exactly what I had in mind!

[kellertuer]

Great! Then I will carefully add the technical details sections for the other solvers as well; probably also for step sizes and debugs.

[kellertuer]

While a few might still be challenging (Chambolle-Pock), I think most (CG, SGD, EPM,...) will just be copies of gradient descent in the technical details. Still good to check them.

And since I am redoing the docs a bit anyways, I will also try to minimise Vale warnings along the way (we at least do not have Vale errors any longer by now).

[kellertuer]

I now added a technical section to all solvers that lists (and currently also explains a bit) which functions are required what for. One could maybe shorten that to just listing functions.

Besides that I will maybe wait a day or two whether vale will get Julia code/docstring support and reiterate here again then. If they are not that fast I might just merge this for now.