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docs/pages.jl

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pages = ["index.md",
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"tutorials/getting_started.md",
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"Tutorials" => Any[
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"tutorials/code_optimization.md",
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"Tutorials" => Any["tutorials/code_optimization.md",
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"tutorials/large_systems.md",
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"tutorials/small_compile.md",
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"tutorials/termination_conditions.md",

docs/src/tutorials/code_optimization.md

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linsolve = LinearSolve.KrylovJL_GMRES()
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sol = solve(prob, NewtonRaphson(; linsolve), reltol = 1e-9)
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```
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```

docs/src/tutorials/getting_started.md

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There are three types of nonlinear systems:
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1. The "standard nonlinear system", i.e. the `NonlinearProblem`. This is a
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system of equations with an initial condition where you want to satisfy
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all equations simultaniously.
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2. The "interval rootfinding problem", i.e. the `IntervalNonlinearProblem`.
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This is the case where you're given an interval `[a,b]` and need to find
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where `f(u) = 0` for `u` inside the bounds.
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3. The "steady state problem", i.e. find the `u` such that `u' = f(u) = 0`.
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While related to (1), it's not entirely the same because there's a uniquely
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defined privledged root.
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4. The nonlinear least squares problem, which is an overconstrained nonlinear
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system (i.e. more equations than states) which might not be satisfiable, i.e.
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there may be no `u` such that `f(u) = 0`, and thus we find the `u` which
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minimizes `||f(u)||` in the least squares sense.
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1. The "standard nonlinear system", i.e. the `NonlinearProblem`. This is a
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system of equations with an initial condition where you want to satisfy
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all equations simultaniously.
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2. The "interval rootfinding problem", i.e. the `IntervalNonlinearProblem`.
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This is the case where you're given an interval `[a,b]` and need to find
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where `f(u) = 0` for `u` inside the bounds.
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3. The "steady state problem", i.e. find the `u` such that `u' = f(u) = 0`.
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While related to (1), it's not entirely the same because there's a uniquely
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defined privledged root.
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4. The nonlinear least squares problem, which is an overconstrained nonlinear
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system (i.e. more equations than states) which might not be satisfiable, i.e.
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there may be no `u` such that `f(u) = 0`, and thus we find the `u` which
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minimizes `||f(u)||` in the least squares sense.
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For now let's focus on the first two. The other two are covered in later tutorials,
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but from the first two we can show the general flow of the NonlinearSolve.jl package.
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Next we can modify the tolerances. Here let's set some really low tolerances to force a tight solution:
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```@example 1
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solve(prob, TrustRegion(), reltol=1e-12, abstol=1e-12)
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solve(prob, TrustRegion(), reltol = 1e-12, abstol = 1e-12)
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```
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There are many more options for doing this configuring. Specifically for handling termination conditions,
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Congrats, you now know how to use the basics of NonlinearSolve.jl! However, there is so much more to
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see. Next check out:
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- [Some code optimization tricks to know about with NonlinearSolve.jl](@ref code_optimization)
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- [An iterator interface which lets you step through the solving process step by step](@ref iterator)
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- [How to handle large systems of equations efficiently](@ref large_systems)
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- [Ways to use NonlinearSolve.jl that is faster to startup and can statically compile](@ref fast_startup)
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- [More detailed termination conditions](@ref termination_conditions_tutorial)
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- [Some code optimization tricks to know about with NonlinearSolve.jl](@ref code_optimization)
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- [An iterator interface which lets you step through the solving process step by step](@ref iterator)
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- [How to handle large systems of equations efficiently](@ref large_systems)
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- [Ways to use NonlinearSolve.jl that is faster to startup and can statically compile](@ref fast_startup)
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- [More detailed termination conditions](@ref termination_conditions_tutorial)
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And also check out the rest of the manual.
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And also check out the rest of the manual.

docs/src/tutorials/iterator_interface.md

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# [Nonlinear Solver Iterator Interface](@id iterator)
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!!! warn
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This iterator interface will be expanded with a `step!` function soon!
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There is an iterator form of the nonlinear solver which mirrors the DiffEq integrator interface:

docs/src/tutorials/small_compile.md

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# Faster Startup and and Static Compilation
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This is a stub article to be completed soon.
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This is a stub article to be completed soon.
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# [More Detailed Termination Conditions](@id termination_conditions_tutorial)
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This is a stub article to be completed soon.
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This is a stub article to be completed soon.

test/basictests.jl

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radius_update_scheme in radius_update_schemes
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probN = NonlinearProblem(quadratic_f, u0, 2.0)
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@test all(solve(probN, TrustRegion(; autodiff, radius_update_scheme)).u .≈ sqrt(2.0))
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@test all(solve(probN, TrustRegion(; autodiff, radius_update_scheme)).u .≈
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sqrt(2.0))
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end
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# Test that `TrustRegion` passes a test that `NewtonRaphson` fails on.

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