Auto-batching Nonlinear Solvers and Beyond

[avik-pal]

Playing around with a new package to generalize the solvers to BatchedArrays. Collecting all the patches here needed to make that work.

• Package for auto-batching -- https://github.com/LuxDL/BatchedArrays.jl (currently private)
  • Think of this as a generalization for SimpleGMRES (batched) and the batched SimpleNonlinearSolve solvers.
• Generalize __init_identity_jacobian and __init_low_rank_jacobian

Example Usage

using NonlinearSolve, BatchedArrays

f(u, p) = u .^ 2 .- p

probB = NonlinearProblem(f, BatchedArray(rand(16, 32), 2.0)  # Solve 32 nonlinear problems simultaneously

solve(probB, NewtonRaphson())

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Comparison is base (0026bc1) 48.24% compared to head (ce3d7aa) 93.94%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #287 +/- ## =========================================== + Coverage 48.24% 93.94% +45.69% =========================================== Files 19 19 Lines 1824 1832 +8 =========================================== + Hits 880 1721 +841 + Misses 944 111 -833 ```

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[avik-pal]

Pulled into other PRs