Use NonlinearAliasSpecifier for NonlinearProblem

[jClugstor]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

This adds support for using the NonlinearAliasSpecifier to specify if u0 is aliased or not.

The reason I want to put it here for now is because with the current way that NonlinearSolve is structured, it would take significant refactoring to do this in a similar way this was done in OrdinaryDiffEq, LinearSolve etc. as well as supporting aliasing other variables. alias_u0 is an argument to many of the internal NonlinearSolve functions, and it would take major changes to change it to using a NonlinearAliasSpecifier, if it even makes sense to do so. Additionally, the __init functions are spread out between the different solving algorithms, so there's no single place in NonlinearSolve to put this, like in the other packages.

This will deprecate the alias_u0 kwarg, and allow users to use a NonlinearAliasSpecifier to specify if u0 is aliased.
A Bool alias kwarg is supported as well.

[ChrisRackauckas]

This is now handled in nonlinearsolvebase?

[jClugstor]

The sensealg part?

[ChrisRackauckas]

No the solve call for NonlinearProblem. https://github.com/SciML/NonlinearSolve.jl/blob/master/lib/NonlinearSolveBase/src/solve.jl#L5

[ChrisRackauckas]

Actually, double check the stack trace during a nonlinearsolve solve? Does it hit here? I thought it was eliminated.

[jClugstor]

It does hit here, unless you use the default solver, so with

using NonlinearSolve

f(u, p) = u .* u .- p
u0 = [1.0, 1.0]
p = 2.0
prob = NonlinearProblem(f, u0, p)
solve(prob)

it hits the __solve for the NonlinearSolvePolyAlgorithm here instead:
https://github.com/SciML/NonlinearSolve.jl/blob/b182ae1b8584763004392b335e094545d9f1be58/lib/NonlinearSolveBase/src/solve.jl#L124-L128

[ChrisRackauckas]

oh I guess we'll move that later.