Use a proper polyalgorithm algorithm type

[avik-pal]

Adding this since it makes it easy to write type-stable polyalgorithms. Once this is in we can simply define a custom polyalgorithm algorithm for https://github.com/SciML/NonlinearSolve.jl/pull/277 as well.

[avik-pal]

I thing that might break is if someone was writing ::RobustMultiNewton. Do we guarantee that the algorithms are types that can be dispatched on?

[codecov[bot]]

Codecov Report

Merging #278 (c5c0176) into master (adc3b31) will decrease coverage by 44.89%. The diff coverage is 55.55%.

@@             Coverage Diff             @@
##           master     #278       +/-   ##
===========================================
- Coverage   93.58%   48.69%   -44.89%     
===========================================
  Files          19       19               
  Lines        1807     1805        -2     
===========================================
- Hits         1691      879      -812     
- Misses        116      926      +810     

Files	Coverage Δ
src/NonlinearSolve.jl	97.10% <ø> (-1.45%)	:arrow_down:
src/default.jl	33.75% <55.55%> (-49.80%)	:arrow_down:

... and 16 files with indirect coverage changes

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[ChrisRackauckas]

no

[avik-pal]

@ChrisRackauckas is the forwarddiff linear solve failure from nonlinear solve or something changed in linear solve?

[ChrisRackauckas]

That's a LinearSolve thing, don't worry about it.

[ChrisRackauckas]

Can you make the 23 tests more robust?

[avik-pal]

Probably disable the GeneralBroyden? It fails only sometimes on CI and locally always passes. I can't even reproduce the failure reliably

[ChrisRackauckas]

Or make it simpler, like number of successes > 5