Better Defaults: Auto AD Selection for Newton Methods

[avik-pal]

• [x] Cleanup the Poly Algorithms
• [x] Proper AD Selection

[ChrisRackauckas]

did you time it at all? It's completely dynamically dispatching and not type stable.

[avik-pal]

Yes not ready yet :sweat:

[avik-pal]

I will loop unroll that version to avoid adding sols for if we add anything to the cache later

[codecov[bot]]

Codecov Report

Merging #244 (91c0ca0) into master (7a5e231) will increase coverage by 7.31%. The diff coverage is 88.63%.

@@            Coverage Diff             @@
##           master     #244      +/-   ##
==========================================
+ Coverage   86.05%   93.37%   +7.31%     
==========================================
  Files          14       14              
  Lines        1205     1147      -58     
==========================================
+ Hits         1037     1071      +34     
+ Misses        168       76      -92     

Files	Coverage Δ
src/dfsane.jl	100.00% <100.00%> (+0.67%)	:arrow_up:
src/gaussnewton.jl	76.19% <100.00%> (+1.19%)	:arrow_up:
src/levenberg.jl	98.46% <100.00%> (+0.03%)	:arrow_up:
src/raphson.jl	100.00% <100.00%> (ø)
src/trustRegion.jl	99.36% <100.00%> (+<0.01%)	:arrow_up:
src/utils.jl	82.85% <95.83%> (+5.07%)	:arrow_up:
src/default.jl	78.48% <79.41%> (+46.20%)	:arrow_up:

... and 1 file with indirect coverage changes

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[avik-pal]

Everything is type-stable to the extent that the output alg is a union type.

[avik-pal]

@ChrisRackauckas this is ready to go in