Introduce a common type for differentiated retractions as vector transport and two such transports for Stiefel

[kellertuer]

Here's my little Christmas project. 🎄
I read a little bit about two new differentiated retractions (they are actually available in ROPTLIB (https://github.com/whuang08/ROPTLIB), but not that well documented.

• Testing
• Check Documentation
• Check whether large interims matrices can be avoided (currently for example d*d' should be 1000x100 for Stiefel(1000,2) which should be avoided by changing order of compuations.

[codecov]

Codecov Report

Merging #318 (c9304b4) into master (a1b604f) will increase coverage by 0.01%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #318      +/-   ##
==========================================
+ Coverage   95.97%   95.99%   +0.01%     
==========================================
  Files          69       69              
  Lines        4646     4667      +21     
==========================================
+ Hits         4459     4480      +21     
  Misses        187      187              

Impacted Files	Coverage Δ
src/Manifolds.jl	100.00% <ø> (ø)
src/manifolds/Stiefel.jl	97.79% <100.00%> (+0.33%)	⬆️
src/tests/tests_general.jl	95.86% <100.00%> (+0.04%)	⬆️

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[mateuszbaran]

The failure on Julia nightly is now caused by this: JuliaPy/PyCall.jl#873 .

[kellertuer]

Thanks for investigating, I did not yet have the time to investigate (and was happy to get pyplot-stuff running in the first place, which took some time and tries).

[mateuszbaran]

No problem, I think it's good to see why nightly builds are failing once in a while.

BTW, I just noticed that the description of scaled transport has some issues: https://juliamanifolds.github.io/Manifolds.jl/previews/PR318/interface.html#ManifoldsBase.ScaledVectorTransport .

[kellertuer]

Thanks for noticing there is a space missing; I will push that fix to master and it will then get into the next version,

[mateuszbaran]

OK, I don't have any other comments here 🙂 .

[kellertuer]

Cool! I just bumped the version and will then merge in a few minutes.