SciML · ChrisRackauckas · Jul 31, 2025 · Jul 31, 2025
diff --git a/docs/make.jl b/docs/make.jl
@@ -51,7 +51,7 @@ makedocs(;
         "https://www.sciencedirect.com/science/article/abs/pii/S0045782523007156",
         "https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd.c",
         "https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrj.c",
-        "https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmder.c",
+        "https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmder.c"
     ],
     checkdocs = :exports,
     warnonly = [:missing_docs],

diff --git a/docs/src/api/scipy.md b/docs/src/api/scipy.md
@@ -19,4 +19,4 @@ Note that using this package requires Python and SciPy to be available via Pytho
 NonlinearSolveSciPy.SciPyLeastSquares
 NonlinearSolveSciPy.SciPyRoot
 NonlinearSolveSciPy.SciPyRootScalar
-```
+```
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
@@ -78,7 +78,8 @@ function brusselator_2d_loop(du, u, p)
     @inbounds for I in CartesianIndices((N, N))
         i, j = Tuple(I)
         x, y = xyd_brusselator[I[1]], xyd_brusselator[I[2]]
-        ip1, im1, jp1, jm1 = limit(i + 1, N), limit(i - 1, N), limit(j + 1, N),
+        ip1, im1, jp1,
+        jm1 = limit(i + 1, N), limit(i - 1, N), limit(j + 1, N),
         limit(j - 1, N)
         du[i, j, 1] = alpha * (u[im1, j, 1] + u[ip1, j, 1] + u[i, jp1, 1] + u[i, jm1, 1] -
                        4u[i, j, 1]) +
@@ -279,7 +280,8 @@ which is more automatic. The setup is very similar to before:
 import AlgebraicMultigrid
 
 function algebraicmultigrid(W, p = nothing)
-    return AlgebraicMultigrid.aspreconditioner(AlgebraicMultigrid.ruge_stuben(convert(AbstractMatrix, W))), LinearAlgebra.I
+    return AlgebraicMultigrid.aspreconditioner(AlgebraicMultigrid.ruge_stuben(convert(AbstractMatrix, W))),
+    LinearAlgebra.I
 end
 
 BenchmarkTools.@btime NLS.solve(prob_brusselator_2d_sparse,

diff --git a/docs/src/tutorials/nonlinear_solve_gpus.md b/docs/src/tutorials/nonlinear_solve_gpus.md
@@ -31,7 +31,7 @@ using the first form.
 In this tutorial we will highlight both use cases in separate parts.
 
 !!! note
-
+    
     If you're looking for GPU-accelerated neural networks inside of nonlinear solvers,
     check out [DeepEquilibriumNetworks.jl](https://docs.sciml.ai/DeepEquilibriumNetworks/stable/).
 
@@ -59,7 +59,7 @@ f(u, p) = u .* u .- p
 u0 = CUDA.cu(ones(1000))
 p = CUDA.cu(collect(1:1000))
 prob = NLS.NonlinearProblem(f, u0, p)
-sol = NLS.solve(prob, NLS.NewtonRaphson(), abstol=1f-4)
+sol = NLS.solve(prob, NLS.NewtonRaphson(), abstol = 1.0f-4)
 ```
 
 Notice a few things here. One, nothing is different except the input array types. But
@@ -95,7 +95,7 @@ import AMDGPU # For if you have an AMD GPU
 import Metal # For if you have a Mac M-series device and want to use the built-in GPU
 import OneAPI # For if you have an Intel GPU
 
-@KernelAbstractions.kernel function parallel_nonlinearsolve_kernel!(result, @Const(prob), @Const(alg))
+KernelAbstractions.@kernel function parallel_nonlinearsolve_kernel!(result, @Const(prob), @Const(alg))
     i = @index(Global)
     prob_i = SciMLBase.remake(prob; p = prob.p[i])
     sol = NLS.solve(prob_i, alg)
@@ -109,7 +109,7 @@ is saying, "for the ith call, get the i'th parameter set and solve with these pa
 The ith result is then this solution".
 
 !!! note
-
+    
     Because kernel code needs to be able to be compiled to a GPU kernel, it has very strict
     specifications of what's allowed because GPU cores are not as flexible as CPU cores.
     In general, this means that you need to avoid any runtime operations in kernel code,
@@ -140,16 +140,16 @@ Now let's build a nonlinear system to test it on.
     out2 = sqrt(p[2]) * (x[3] - x[4])
     out3 = (x[2] - p[3] * x[3])^2
     out4 = sqrt(p[4]) * (x[1] - x[4]) * (x[1] - x[4])
-    StaticArrays.SA[out1,out2,out3,out4]
+    StaticArrays.SA[out1, out2, out3, out4]
 end
 
 p = StaticArrays.@SVector [StaticArrays.@SVector(rand(Float32, 4)) for _ in 1:1024]
-u0 = StaticArrays.SA[1f0, 2f0, 3f0, 4f0]
+u0 = StaticArrays.SA[1.0f0, 2.0f0, 3.0f0, 4.0f0]
 prob = SciMLBase.ImmutableNonlinearProblem{false}(p2_f, u0, p)
 ```
 
 !!! note
-
+    
     Because the custom kernel is going to need to embed the the code for our nonlinear
     problem into the kernel, it also must be written to be GPU compatible.
     In general, this means that you need to avoid any runtime operations in kernel code,
@@ -176,4 +176,5 @@ vectorized_solve(prob, NLS.SimpleNewtonRaphson(); backend = Metal.MetalBackend()
 ```
 
 !!! warn
+
     The GPU-based calls will only work on your machine if you have a compatible GPU!
diff --git a/docs/src/tutorials/optimizing_parameterized_ode.md b/docs/src/tutorials/optimizing_parameterized_ode.md
@@ -53,7 +53,8 @@ nlls_prob = NLS.NonlinearLeastSquaresProblem(loss_function, p_init, vec(reduce(h
 Now, we can use any NLLS solver to solve this problem.
 
 ```@example parameterized_ode
-res = NLS.solve(nlls_prob, NLS.LevenbergMarquardt(); maxiters = 1000, show_trace = Val(true),
+res = NLS.solve(
+    nlls_prob, NLS.LevenbergMarquardt(); maxiters = 1000, show_trace = Val(true),
     trace_level = NLS.TraceWithJacobianConditionNumber(25))
 nothing # hide
 ```

diff --git a/docs/src/tutorials/snes_ex2.md b/docs/src/tutorials/snes_ex2.md
@@ -38,7 +38,8 @@ details.
 
 ```@example snes_ex2
 nlfunc_dense = NLS.NonlinearFunction(form_residual!)
-nlfunc_sparse = NLS.NonlinearFunction(form_residual!; sparsity = SparseConnectivityTracer.TracerSparsityDetector())
+nlfunc_sparse = NLS.NonlinearFunction(
+    form_residual!; sparsity = SparseConnectivityTracer.TracerSparsityDetector())
 
 nlprob_dense = NLS.NonlinearProblem(nlfunc_dense, u0)
 nlprob_sparse = NLS.NonlinearProblem(nlfunc_sparse, u0)

diff --git a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
@@ -21,7 +21,8 @@ function SciMLBase.__solve(
         termination_condition, alg
     )
 
-    f_wrapped, u, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+    f_wrapped, u,
+    resid = NonlinearSolveBase.construct_extension_function_wrapper(
         prob; alias_u0, can_handle_oop = Val(prob.u0 isa SArray)
     )
     f = if prob.u0 isa SArray
@@ -49,7 +50,8 @@ function SciMLBase.__solve(
     )
 
     if prob.u0 isa SArray
-        res, fx, info, iter, nfev, njev = FastLM.lmsolve(
+        res, fx, info, iter, nfev,
+        njev = FastLM.lmsolve(
             f, jac_fn, prob.u0; solver_kwargs...
         )
         LM, solver = nothing, nothing
@@ -68,7 +70,8 @@ function SciMLBase.__solve(
 
         LM = FastLM.LMWorkspace(u, resid, J)
 
-        res, fx, info, iter, nfev, njev, LM, solver = FastLM.lmsolve!(
+        res, fx, info, iter, nfev, njev,
+        LM, solver = FastLM.lmsolve!(
             f, jac_fn, LM; solver, solver_kwargs...
         )
     end

diff --git a/ext/NonlinearSolveFixedPointAccelerationExt.jl b/ext/NonlinearSolveFixedPointAccelerationExt.jl
@@ -15,7 +15,8 @@ function SciMLBase.__solve(
         termination_condition, alg
     )
 
-    f, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+    f, u0,
+    resid = NonlinearSolveBase.construct_extension_function_wrapper(
         prob; alias_u0, make_fixed_point = Val(true), force_oop = Val(true)
     )
 

diff --git a/ext/NonlinearSolveMINPACKExt.jl b/ext/NonlinearSolveMINPACKExt.jl
@@ -17,7 +17,8 @@ function SciMLBase.__solve(
         termination_condition, alg
     )
 
-    f_wrapped!, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+    f_wrapped!, u0,
+    resid = NonlinearSolveBase.construct_extension_function_wrapper(
         prob; alias_u0
     )
     resid_size = size(resid)

diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
@@ -33,7 +33,8 @@ function SciMLBase.__solve(
             prob.f, autodiff, prob.u0, Constant(prob.p)
         )
 
-        fj_scalar = @closure (Jx, x) -> begin
+        fj_scalar = @closure (Jx,
+            x) -> begin
             return DifferentiationInterface.value_and_derivative(
                 prob.f, prep, autodiff, x, Constant(prob.p)
             )

diff --git a/ext/NonlinearSolvePETScExt.jl b/ext/NonlinearSolvePETScExt.jl
@@ -22,7 +22,8 @@ function SciMLBase.__solve(
         termination_condition, alg; abs_norm_supported = false
     )
 
-    f_wrapped!, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+    f_wrapped!, u0,
+    resid = NonlinearSolveBase.construct_extension_function_wrapper(
         prob; alias_u0
     )
     T = eltype(u0)
@@ -48,7 +49,9 @@ function SciMLBase.__solve(
 
     nf = Ref{Int}(0)
 
-    f! = @closure (cfx, cx, user_ctx) -> begin
+    f! = @closure (cfx,
+        cx,
+        user_ctx) -> begin
         nf[] += 1
         fx = cfx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cfx; read = false) : cfx
         x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
@@ -76,7 +79,8 @@ function SciMLBase.__solve(
             )
             J_init = zeros(T, 1, 1)
         else
-            jac!, J_init = NonlinearSolveBase.construct_extension_jac(
+            jac!,
+            J_init = NonlinearSolveBase.construct_extension_jac(
                 prob, alg, u0, resid; autodiff, initial_jacobian = Val(true)
             )
         end
@@ -85,7 +89,10 @@ function SciMLBase.__solve(
 
         if J_init isa AbstractSparseMatrix
             PJ = PETSc.MatSeqAIJ(J_init)
-            jac_fn! = @closure (cx, J, _, user_ctx) -> begin
+            jac_fn! = @closure (cx,
+                J,
+                _,
+                user_ctx) -> begin
                 njac[] += 1
                 x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
                 if J isa PETSc.AbstractMat
@@ -102,7 +109,10 @@ function SciMLBase.__solve(
             snes.user_ctx = (; jacobian = J_init)
         else
             PJ = PETSc.MatSeqDense(J_init)
-            jac_fn! = @closure (cx, J, _, user_ctx) -> begin
+            jac_fn! = @closure (cx,
+                J,
+                _,
+                user_ctx) -> begin
                 njac[] += 1
                 x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
                 jac!(J, x)

diff --git a/ext/NonlinearSolveSIAMFANLEquationsExt.jl b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
@@ -64,7 +64,8 @@ function SciMLBase.__solve(
         elseif method == :secant
             sol = secant(f, prob.u0; maxit = maxiters, atol, rtol, printerr)
         elseif method == :anderson
-            f_aa, u, _ = NonlinearSolveBase.construct_extension_function_wrapper(
+            f_aa, u,
+            _ = NonlinearSolveBase.construct_extension_function_wrapper(
                 prob; alias_u0, make_fixed_point = Val(true)
             )
             sol = aasol(
@@ -73,7 +74,8 @@ function SciMLBase.__solve(
             )
         end
     else
-        f, u, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+        f, u,
+        resid = NonlinearSolveBase.construct_extension_function_wrapper(
             prob; alias_u0, make_fixed_point = Val(method == :anderson)
         )
         N = length(u)

diff --git a/ext/NonlinearSolveSpeedMappingExt.jl b/ext/NonlinearSolveSpeedMappingExt.jl
@@ -16,7 +16,8 @@ function SciMLBase.__solve(
         termination_condition, alg
     )
 
-    m!, u, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+    m!, u,
+    resid = NonlinearSolveBase.construct_extension_function_wrapper(
         prob; alias_u0, make_fixed_point = Val(true)
     )
     tol = NonlinearSolveBase.get_tolerance(abstol, eltype(u))

diff --git a/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl b/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl
@@ -7,7 +7,9 @@ using SciMLBase: SciMLBase, IntervalNonlinearProblem
 
 using BracketingNonlinearSolve: Bisection, Brent, Alefeld, Falsi, ITP, Ridder
 
-const DualIntervalNonlinearProblem{T, V, P} = IntervalNonlinearProblem{
+const DualIntervalNonlinearProblem{T,
+    V,
+    P} = IntervalNonlinearProblem{
     uType, iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
 } where {uType, iip}
 

diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -29,17 +29,17 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, nothing, args...; kwa
     return CommonSolve.solve(prob, ITP(), args...; kwargs...)
 end
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, 
+function CommonSolve.solve(prob::IntervalNonlinearProblem,
         alg::AbstractBracketingAlgorithm, args...; sensealg = nothing, kwargs...)
-    return bracketingnonlinear_solve_up(prob::IntervalNonlinearProblem, sensealg, prob.p, alg, args...; kwargs...)
+    return bracketingnonlinear_solve_up(
+        prob::IntervalNonlinearProblem, sensealg, prob.p, alg, args...; kwargs...)
 end
 
-
-function bracketingnonlinear_solve_up(prob::IntervalNonlinearProblem, sensealg, p, alg, args...; kwargs...)
+function bracketingnonlinear_solve_up(
+        prob::IntervalNonlinearProblem, sensealg, p, alg, args...; kwargs...)
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
 
-
 @setup_workload begin
     for T in (Float32, Float64)
         prob_brack = IntervalNonlinearProblem{false}(

diff --git a/lib/BracketingNonlinearSolve/src/bisection.jl b/lib/BracketingNonlinearSolve/src/bisection.jl
@@ -86,7 +86,8 @@ function SciMLBase.__solve(
         i += 1
     end
 
-    sol, i, left, right, fl, fr = Impl.bisection(
+    sol, i, left, right,
+    fl, fr = Impl.bisection(
         left, right, fl, fr, f, abstol, maxiters - i, prob, alg
     )
 

diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -118,7 +118,8 @@ function SciMLBase.__solve(
         i += 1
     end
 
-    sol, i, left, right, fl, fr = Impl.bisection(
+    sol, i, left, right,
+    fl, fr = Impl.bisection(
         left, right, fl, fr, f, abstol, maxiters - i, prob, alg
     )
 

diff --git a/lib/BracketingNonlinearSolve/src/falsi.jl b/lib/BracketingNonlinearSolve/src/falsi.jl
@@ -76,7 +76,8 @@ function SciMLBase.__solve(
         i += 1
     end
 
-    sol, i, left, right, fl, fr = Impl.bisection(
+    sol, i, left, right,
+    fl, fr = Impl.bisection(
         left, right, fl, fr, f, abstol, maxiters - i, prob, alg
     )
 

diff --git a/lib/BracketingNonlinearSolve/src/ridder.jl b/lib/BracketingNonlinearSolve/src/ridder.jl
@@ -90,7 +90,8 @@ function SciMLBase.__solve(
         i += 1
     end
 
-    sol, i, left, right, fl, fr = Impl.bisection(
+    sol, i, left, right,
+    fl, fr = Impl.bisection(
         left, right, fl, fr, f, abstol, maxiters - i, prob, alg
     )
 

diff --git a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
@@ -18,7 +18,7 @@ end
 
         @testset for p in 1.1:0.1:100.0
             @test g(p)≈sqrt(p) atol=1e-3 rtol=1e-3
-            @test ForwardDiff.derivative(g, p)≈1 / (2 * sqrt(p)) atol=1e-3 rtol=1e-3
+            @test ForwardDiff.derivative(g, p)≈1/(2*sqrt(p)) atol=1e-3 rtol=1e-3
         end
 
         t = (p) -> [sqrt(p[2] / p[1])]
@@ -30,7 +30,7 @@ end
             return [sol.u]
         end
 
-        @test g2(p)≈[sqrt(p[2] / p[1])] atol=1e-3 rtol=1e-3
+        @test g2(p)≈[sqrt(p[2]/p[1])] atol=1e-3 rtol=1e-3
         @test ForwardDiff.jacobian(g2, p)≈ForwardDiff.jacobian(t, p) atol=1e-3 rtol=1e-3
 
         probB = IntervalNonlinearProblem{false}(quadratic_f, (1.0, 2.0), 2.0)
@@ -50,8 +50,8 @@ end
 end
 
 @testitem "Tolerance Tests Interval Methods" setup=[RootfindingTestSnippet] tags=[:core] begin
-    prob = IntervalNonlinearProblem(quadratic_f, (1.0, 20.0), 2.0)
-    ϵ = eps(Float64) # least possible tol for all methods
+    prob=IntervalNonlinearProblem(quadratic_f, (1.0, 20.0), 2.0)
+    ϵ=eps(Float64) # least possible tol for all methods
 
     @testset for alg in (Bisection(), Falsi(), ITP(), Muller(), nothing)
         @testset for abstol in [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6]

diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -124,7 +124,8 @@ for algType in GENERAL_SOLVER_TYPES
     @eval function SciMLBase.__solve(
             prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
     )
-        sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+        sol,
+        partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
             prob, alg, args...; kwargs...
         )
         dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)

diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -17,7 +17,7 @@ using EnzymeCore: EnzymeCore
 using MaybeInplace: @bb
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
-                 AbstractNonlinearAlgorithm, 
+                 AbstractNonlinearAlgorithm,
                  NonlinearProblem, NonlinearLeastSquaresProblem,
                  NonlinearFunction, NLStats, LinearProblem,
                  LinearAliasSpecifier, ImmutableNonlinearProblem
@@ -71,7 +71,7 @@ include("forward_diff.jl")
 @compat(public, (construct_jacobian_cache,))
 @compat(public,
     (assert_extension_supported_termination_condition,
-        construct_extension_function_wrapper, construct_extension_jac))
+    construct_extension_function_wrapper, construct_extension_jac))
 
 export TraceMinimal, TraceWithJacobianConditionNumber, TraceAll