refactor: use DI.jl for the jacobian stuff

SciML / NonlinearSolve.jl

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

https://docs.sciml.ai/NonlinearSolve/stable/

MIT License

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refactor: use DI.jl for the jacobian stuff #467

Closed avik-pal closed 1 week ago

avik-pal commented 1 week ago

cleaned up the scalar stuff. fixes #451
partially addresses https://github.com/SciML/NonlinearSolve.jl/issues/415. For now we use the dense AD from DI