Created
October 21, 2025 21:36
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MWE for issue with SCT+Nonlinear solve
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| module MWE_DI | |
| using DifferentiationInterface | |
| using NonlinearSolve | |
| using SparseConnectivityTracer | |
| using SparseMatrixColorings | |
| struct System{Tprep} | |
| X::Vector{Float64} | |
| jac_prep::Tprep | |
| end | |
| function unknowns(sys::System, value = 0.0) | |
| u = copy(sys.X) | |
| u .= value | |
| return u | |
| end | |
| function operator!(f, u, sys) | |
| (; X) = sys | |
| n = length(X) | |
| f .= zero(eltype(f)) | |
| for i in 1:(n - 1) | |
| du = (u[i + 1] - u[i]) / (X[i + 1] - X[i]) | |
| f[i] += du | |
| f[i + 1] -= du | |
| end | |
| for i in 1:n | |
| f[i] += 0.1 * u[i] - 1 | |
| end | |
| return f | |
| end | |
| function SystemSCT(X) | |
| X = collect(X) | |
| protosys = System(X, nothing) | |
| input = unknowns(protosys, 1) | |
| output = unknowns(protosys) | |
| backend = AutoSparse( | |
| AutoForwardDiff(); | |
| sparsity_detector = TracerSparsityDetector(), | |
| coloring_algorithm = GreedyColoringAlgorithm() | |
| ) | |
| jac_prep = prepare_jacobian( | |
| (f, u) -> operator!(f, u, protosys), | |
| output, | |
| backend, | |
| input; | |
| strict = Val(false) | |
| ) | |
| return System(X, jac_prep) | |
| end | |
| function SystemADT(X) | |
| X = collect(X) | |
| protosys = System(X, nothing) | |
| input = unknowns(protosys, 1) | |
| output = unknowns(protosys) | |
| sparsity = ADTypes.jacobian_sparsity( | |
| (f, u) -> operator!(f, u, protosys), | |
| output, | |
| input, | |
| TracerSparsityDetector() | |
| ) | |
| return System(X, sparsity) | |
| end | |
| function testSCT(; withprototype = false) | |
| sys = SystemSCT(range(0, 1, length = 11)) | |
| if withprototype | |
| nlfunc = NonlinearFunction(operator!, jac_prototype = sys.jac_prep.sparsity) | |
| else | |
| nlfunc = NonlinearFunction(operator!) | |
| end | |
| prob = NonlinearProblem(nlfunc, unknowns(sys, 0.5), sys) | |
| return solve(prob, NewtonRaphson()) | |
| end | |
| function testADT(; withprototype = false) | |
| sys = SystemADT(range(0, 1, length = 11)) | |
| if withprototype | |
| nlfunc = NonlinearFunction(operator!, jac_prototype = sys.jac_prep) | |
| else | |
| nlfunc = NonlinearFunction(operator!) | |
| end | |
| prob = NonlinearProblem(nlfunc, unknowns(sys, 0.5), sys) | |
| return solve(prob, NewtonRaphson()) | |
| end | |
| end |
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