Rework presentation of keywords

[kellertuer]

This is heavily WIP (just had a bit on time on the train with not so much concentration).

This aims to

• find a format for keyword arguments that is better readable in both the rendered docs and REPL
• -> for not I have a newline too much in the HTML format (hence rendering it here might be nice)
• indicate defaults for keywords is for now done with an emoji in the last line (a bit too much offset for now).

🛣️ Roadmap

• [x] find a better way of presenting keyword arguments
• [x] start collecting common keywords and their defaults in a central “string collection” to reduce duplication in strings (and hence avoid possible multiple typos / indifferences when updating parts)
• rework solver interfaces
  • [x] plans/
  • solvers/
  • [x] ARC and its sub solvers, especially Lanczos
  • [x] ALM
  • [x] Chambolle-Pock
  • [x] CG
  • [x] CBM
  • [x] CPPA
  • [x] DoC
  • [x] DCPPA
  • [x] DR
  • [x] EPM
  • [x] Frank_Wolfe_method and its state
  • [x] gradient_descent and its state
  • [x] LM
  • [x] NM
  • [x] PSO
  • [x] PDRSNA
  • [x] PBM
  • [x] QN
  • [x] TCG
  • [x] SGM
  • [x] Stochastic Gradient
  • [x] TR
  • [x] conjugate residual (and its plan)
  • [x] interior point newton (and its plan)
• generally
  • [x] work through replaces `:(\s+)\(`(.*)`\) to =$2`: (maybe with a newline)
  • [x] similarly for `:(\s+)\([`(.*)`\)` (keyword with linking examples
  • Introduce Documenterinterlinks for the functions (after most doc strings are no longer raw)
    • [x] default_retraction_method
    • [x] default_inverse_retraction_method
    • [x] zero_vector
    • [x] rand
    • [x] at_iteration field should be unified
  • unify use of indices
    • [x] k for iterations
    • [x] I for inequality constraints g_i
    • [x] j for equality constraints h_j
  • [x] carefully check to add more links e.g. for
    • [x] get_gradient
    • [x] get_cost
    • [x] get_iterate
  • [x] extend the Nelder-Mead documentation and write down the whole algorithm in the doc string.
  • [x] check and fix why it seems that :WhenActive is broken in https://manoptjl.org/stable/tutorials/HowToDebug/#Subsolver-debug

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 99.71014% with 1 line in your changes missing coverage. Please review.

Project coverage is 99.76%. Comparing base (489da96) to head (65d6381).

Files	Patch %	Lines
src/solvers/adaptive_regularization_with_cubics.jl	66.66%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #393 +/- ## ========================================== - Coverage 99.78% 99.76% -0.02% ========================================== Files 76 77 +1 Lines 8226 8256 +30 ========================================== + Hits 8208 8237 +29 - Misses 18 19 +1 ```

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[kellertuer]

I think I found a good format by now and with the snippets we also avoid “stringduplication” – that is for example the “first parameter is a manifold” text will soon be the same in all doc strings.

[kellertuer]

I think I have converged to a nice new format, and with a bit of rewriting how the doc string is defined, this allows to reuse parts as well – for example prominent keywords like evaluation=

Format

* `keyword=default`:
  description

is nice, since the = also indicates that what follows is the default. All doc strings will be reformulated as “non-raw” to allow for interpolation. this means raw parts, like formulae, should be defined before.

Now that this is clear, this PR is really just a large work to check all doc strings and reform them. But the benefit is, that this reduces a lot of duplication in the strings as well, since common tens are now defined in plans/docstring_snippets.jl both lines – the keyword=default and the description are possible strings to be collected, whenever used more than once or twice.

Still a bit of work to do, where I will try to work on a doc string every day.

[kellertuer]

So now this should be good to go. Not sure it is worth its own version, since I will not activate vale (basically text style check) for now, since they have too often breaking changes and though I implemented Julia code stuff for them the newest version reports, .jl files are not allowed in checks.

[kellertuer]

Since this is really just involving doc string rewrites, I will merge this now and include it in the next release (the other PR still open). It will hence already reside on master for a while then (without a new version).