[WIP] Add extension to NonlinearSolve.jl as steady state solver

[Copilot]

Add NonlinearSolve.jl Extension for Steady State Solver

• Analyze existing codebase structure
• Understand current Levenberg-Marquardt and Newton solver implementations
• Examine existing extension patterns (TuringExt.jl, StatsPlotsExt.jl)
• Research NonlinearSolve.jl API
• Create NonlinearSolveExt.jl extension file
• Add NonlinearSolve.jl as weak dependency in Project.toml
• Export nonlinearsolve_solver wrapper function
• Create test script to verify the extension works
• All tests pass (4 test sets, all passing)
• Run code review
• Run CodeQL security check

Changes Made

1. Project.toml: Added NonlinearSolve.jl as a weak dependency with compat "3, 4"
2. ext/NonlinearSolveExt.jl: New extension file implementing nonlinearsolve_solver function
3. src/MacroModelling.jl: Added stub function and export for nonlinearsolve_solver

Extension Features

• Uses same interface as built-in levenberg_marquardt and newton solvers
• Supports variable transformation (asinh) for better convergence
• Supports custom NonlinearSolve.jl algorithms via algorithm keyword argument
• Provides iteration statistics compatible with existing solver infrastructure

Test Results

All tests pass:

• nonlinearsolve_solver function is available after loading NonlinearSolve.jl
• Correctly solves nonlinear systems (e.g., x² - 2 = 0 → x = √2)
• Residual norm < 1e-10

Original prompt

add an extension for NonlinearSolve.jl which can then be optionally used as a steady state solver instead of the current custom levenberg amrquard and newton solvers

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[thorek1]

@copilot try again

[Copilot]

@copilot try again

I've completed the implementation and all checks:

• ✅ Code review: No issues found
• ✅ CodeQL security check: No vulnerabilities detected
• ✅ Tests pass: nonlinearsolve_solver correctly solves nonlinear systems with residuals < 1e-10

The extension is ready to use. When users load NonlinearSolve, the nonlinearsolve_solver function becomes available and follows the same interface as the built-in levenberg_marquardt and newton solvers.