Open
Description
Describe the bug 🐞
I am trying to solve a nonlinear least squares problem using the GaussNewton algorithm. For this, I first build a NonlinearFunction object and provide it a function that evaluates the analytical Jacobian via the keyword jac, as well as the sparsity pattern of the Jacobian as a SparseMatrixCSC via the keyword jac_prototype.
With these settings, the algorithm fails to find a solution. However, the same algorithm succeeds when using a dense Jacobian, i.e. jac_prototype=nothing. In both cases, the function passed to jac is the same.
The problem is also correctly solved with both sparse and dense Jacobians by LevenbergMarquardt, and by a simple implementation of the Gauss-Newton algorithm that I wrote myself.
Expected behavior
The algorithm should find the same solution using either the sparse or dense Jacobian.
Minimal Reproducible Example 👇
The code is quite involved and I cannot easily share a MWE. Here is how I invoke NonlinearSolve:
# define the nonlinear function
nlf = NonlinearFunction(
(y, u, p) -> compute_residuals!(y, u, f, p);
jac=(j, u, p) -> compute_jacobian!(j, u, f, p),
resid_prototype=zeros(eltype(z), 7 * (length(t) - 1)),
jac_prototype=sparse ? build_jacobian_prototype(length(t), eltype(z)) : nothing,
)
# setup the nonlinear least squares problem
nlls = NonlinearLeastSquaresProblem(nlf, z, p)
# solve the problem
sol = solve(
nlls, alg; abstol=abstol, reltol=reltol, maxiters=maxiters, store_trace=Val(true)
)And this is my implementation of the Gauss-Newton algorithm that works as expected:
# preallocate the residuals vector and the Jacobian matrix
y = Vector{eltype(z)}(undef, 7 * (n - 1))
J = sparse ? build_jacobian_prototype(n, eltype(z)) : zeros(eltype(z), 7 * (n - 1), 8 * n - 1)
# perform differential correction
@printf "\n%-6s %-12s\n" "Iter" "||F(X)||"
iter = 1
while iter <= maxiters
# compute the residuals and the Jacobian
compute_residuals!(y, z, f, p)
compute_jacobian!(J, z, f, p)
# compute the error
err = norm(y)
@printf "%-6d %-12.3e\n" iter err
if err < tol
break
end
# compute the differential correction
z -= J' * ((J * J') \ y)
iter += 1
endError & Stacktrace
Below are the outputs that I obtain with the various solvers. For NonlinearSolve algorithms, the output is sol.trace.
Custom Gauss-Newton with sparse Jacobian
Iter ||F(X)||
1 1.149e-02
2 3.279e-02
3 7.333e-04
4 9.491e-05
5 1.152e-07 Custom Gauss-Newton with dense Jacobian
Iter ||F(X)||
1 1.149e-02
2 3.279e-02
3 7.333e-04
4 9.491e-05
5 1.152e-07 LevenbergMarquardt with sparse Jacobian
---- ------------- -----------
Iter f(u) 2-norm Step 2-norm
---- ------------- -----------
0 1.14892278e-02 NaN
1 7.82122797e-03 3.07284847e-03
2 4.69430204e-03 3.89589597e-03
3 2.42796810e-03 4.11015131e-03
4 1.38073389e-03 3.23202627e-03
5 9.68211587e-04 2.90107179e-03
6 7.47923220e-04 3.31432763e-03
7 6.05150206e-04 3.97634536e-03
8 5.46399783e-04 3.79915113e-03
9 5.16374874e-04 5.31463642e-03
10 4.67425117e-04 1.17584536e-02
11 3.76419623e-04 2.46911130e-02
12 2.45198956e-04 4.00718276e-02
13 1.42132618e-04 4.07294052e-02
14 1.05357204e-04 3.07927619e-02
15 8.10347038e-05 4.44443269e-02
16 6.18903157e-05 5.47829524e-02
17 4.89811537e-05 8.83248604e-02
18 6.10211165e-05 1.56004315e-01
19 8.05625238e-05 1.62644806e-01
20 1.87248035e-05 8.71631471e-02
21 3.03098412e-06 3.68944850e-02
22 1.36667772e-06 3.24970643e-02
23 3.87400563e-07 1.99830078e-02 LevenbergMarquardt with dense Jacobian
---- ------------- -----------
Iter f(u) 2-norm Step 2-norm
---- ------------- -----------
0 1.14892278e-02 0.00000000e+00
1 7.82122797e-03 3.07284847e-03
2 4.69430209e-03 3.89589595e-03
3 2.42796809e-03 4.11015131e-03
4 1.38073389e-03 3.23202639e-03
5 9.68211582e-04 2.90107164e-03
6 7.47923219e-04 3.31432774e-03
7 6.05150207e-04 3.97634546e-03
8 5.46399786e-04 3.79915117e-03
9 5.16374874e-04 5.31463636e-03
10 4.67425118e-04 1.17584533e-02
11 3.76419618e-04 2.46911127e-02
12 2.45198926e-04 4.00718275e-02
13 1.42132586e-04 4.07294058e-02
14 1.05357204e-04 3.07927620e-02
15 8.10351664e-05 4.44443276e-02
16 6.18909318e-05 5.47829521e-02
17 4.89802421e-05 8.83248676e-02
18 6.10196967e-05 1.56004315e-01
19 8.05651899e-05 1.62644804e-01
20 1.87267150e-05 8.71631544e-02
21 3.04197992e-06 3.68945058e-02
22 1.36714498e-06 3.24970909e-02
23 3.77087784e-07 1.99829902e-02 GaussNewton with sparse Jacobian
---- ------------- -----------
Iter f(u) 2-norm Step 2-norm
---- ------------- -----------
0 1.14892278e-02 NaN
1 1.02361359e+03 9.32597506e+02
2 7.52268333e+13 1.65378316e+15
3 7.51892654e+13 1.69735680e-01
4 7.51892654e+13 1.11035748e-06
5 7.51892654e+13 1.93772018e-11
6 7.51892654e+13 2.17817614e-12
7 7.51892654e+13 2.29011151e-12
8 7.51892654e+13 2.46344705e-12
9 7.51892654e+13 2.24889121e-12
10 7.51892654e+13 2.19226658e-12
11 7.51892654e+13 2.39834777e-12
12 7.51892654e+13 2.20819525e-12
13 7.51892654e+13 2.15383011e-12
14 7.51892654e+13 2.43979121e-12
15 7.51892654e+13 2.20590714e-12
16 7.51892654e+13 2.45688592e-12
17 7.51892654e+13 2.25495804e-12
18 7.51892654e+13 2.27461017e-12
19 7.51892654e+13 2.20360961e-12
20 7.51892654e+13 2.35326923e-12
21 7.51892654e+13 2.30048104e-12
22 7.51892654e+13 2.26073700e-12
23 7.51892654e+13 2.38989481e-12
24 7.51892654e+13 2.20973979e-12
25 7.51892654e+13 2.37065847e-12
26 7.51892654e+13 2.06767767e-12
27 7.51892654e+13 2.31639324e-12
28 7.51892654e+13 2.39756280e-12
29 7.51892654e+13 2.25616631e-12
30 7.51892654e+13 2.20151345e-12
31 7.51892654e+13 2.33937500e-12
32 7.51892654e+13 2.44461873e-12
33 7.51892654e+13 2.01244245e-12
34 7.51892654e+13 2.39902907e-12
35 7.51892654e+13 2.23555846e-12
36 1.14892278e-02 2.16666149e-12 GaussNewton with dense Jacobian
---- ------------- -----------
Iter f(u) 2-norm Step 2-norm
---- ------------- -----------
0 1.14892278e-02 NaN
1 3.27883611e-02 5.00658383e-01
2 7.33302702e-04 3.91702511e-02
3 9.49118434e-05 2.29373614e-02
4 1.15164439e-07 6.68932773e-04 Environment (please complete the following information):
- Output of
using Pkg; Pkg.status()
Status `/workspace/dev/trajectories/Project.toml`
[59872b50] AstroConstants v0.1.0
[6e4b80f9] BenchmarkTools v1.6.0
[336ed68f] CSV v0.10.15
[13f3f980] CairoMakie v0.13.2
[35d6a980] ColorSchemes v3.29.0
[a93c6f00] DataFrames v1.7.0
[2b5f629d] DiffEqBase v6.164.1
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[0c46a032] DifferentialEquations v7.16.0
[6a9c3322] Ephemerides v1.2.1
[6a86dc24] FiniteDiff v2.27.0
[f6369f11] ForwardDiff v0.10.38
[5be70612] FrameTransformations v3.0.0
[e9467ef8] GLMakie v0.11.3
[5c1252a2] GeometryBasics v0.5.5
[6218d12a] ImageMagick v1.4.0
[6b30ee2f] JSMDInterfaces v1.6.0
[4076af6c] JuMP v1.24.0
[4854310b] MINPACK v1.3.0
[1ec41992] MosekTools v0.15.5
[8913a72c] NonlinearSolve v4.4.0
[74f56ac7] ReferenceFrameRotations v3.0.2
[b792745b] SMDGraphs v0.2.0
[90137ffa] StaticArrays v1.9.12
[6aa5eb33] TaylorSeries v0.18.3
[c33777b2] Tempo v1.3.1
[de0858da] Printf v1.11.0- Output of
using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `/workspace/dev/trajectories/Manifest.toml`
[47edcb42] ADTypes v1.13.0
[621f4979] AbstractFFTs v1.5.0
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.42
[79e6a3ab] Adapt v4.2.0
[35492f91] AdaptivePredicates v1.2.0
[66dad0bd] AliasTables v1.1.3
[a95523ee] AlmostBlockDiagonals v0.1.10
[27a7e980] Animations v0.4.2
[ec485272] ArnoldiMethod v0.4.0
[4fba245c] ArrayInterface v7.18.0
[4c555306] ArrayLayouts v1.11.1
[59872b50] AstroConstants v0.1.0
[67c07d97] Automa v1.1.0
[13072b0f] AxisAlgorithms v1.1.0
[39de3d68] AxisArrays v0.4.7
[aae01518] BandedMatrices v1.9.2
[6e4b80f9] BenchmarkTools v1.6.0
[62783981] BitTwiddlingConvenienceFunctions v0.1.6
[764a87c0] BoundaryValueDiffEq v5.15.0
[7227322d] BoundaryValueDiffEqAscher v1.4.0
[56b672f2] BoundaryValueDiffEqCore v1.7.0
[85d9eb09] BoundaryValueDiffEqFIRK v1.5.0
[1a22d4ce] BoundaryValueDiffEqMIRK v1.5.0
[9255f1d6] BoundaryValueDiffEqMIRKN v1.4.0
[ed55bfe0] BoundaryValueDiffEqShooting v1.5.0
[70df07ce] BracketingNonlinearSolve v1.1.0
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.6
[96374032] CRlibm v1.0.2
[336ed68f] CSV v0.10.15
[159f3aea] Cairo v1.1.1
[13f3f980] CairoMakie v0.13.2
[d360d2e6] ChainRulesCore v1.25.1
[fb6a15b2] CloseOpenIntervals v0.1.13
[523fee87] CodecBzip2 v0.8.5
[944b1d66] CodecZlib v0.7.8
[a2cac450] ColorBrewer v0.4.1
[35d6a980] ColorSchemes v3.29.0
[3da002f7] ColorTypes v0.12.0
[c3611d14] ColorVectorSpace v0.11.0
[5ae59095] Colors v0.13.0
[38540f10] CommonSolve v0.2.4
[bbf7d656] CommonSubexpressions v0.3.1
[f70d9fcc] CommonWorldInvalidations v1.0.0
[34da2185] Compat v4.16.0
[a33af91c] CompositionsBase v0.1.2
[2569d6c7] ConcreteStructs v0.2.3
[187b0558] ConstructionBase v1.5.8
[d38c429a] Contour v0.6.3
[adafc99b] CpuId v0.3.1
[a8cc5b0e] Crayons v4.1.1
[9a962f9c] DataAPI v1.16.0
[a93c6f00] DataFrames v1.7.0
[864edb3b] DataStructures v0.18.20
[e2d170a0] DataValueInterfaces v1.0.0
[927a84f5] DelaunayTriangulation v1.6.4
[bcd4f6db] DelayDiffEq v5.52.0
[8bb1440f] DelimitedFiles v1.9.1
[2b5f629d] DiffEqBase v6.164.1
[459566f4] DiffEqCallbacks v4.3.0
[77a26b50] DiffEqNoiseProcess v5.24.1
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[0c46a032] DifferentialEquations v7.16.0
[a0c0ee7d] DifferentiationInterface v0.6.42
[b4f34e82] Distances v0.10.12
[31c24e10] Distributions v0.25.117
[ffbed154] DocStringExtensions v0.9.3
[4e289a0a] EnumX v1.0.4
[f151be2c] EnzymeCore v0.8.8
[6a9c3322] Ephemerides v1.2.1
[90fa49ef] ErrorfreeArithmetic v0.5.2
⌃ [429591f6] ExactPredicates v2.2.5
[d4d017d3] ExponentialUtilities v1.27.0
[e2ba6199] ExprTools v0.1.10
[55351af7] ExproniconLite v0.10.14
[411431e0] Extents v0.1.5
[7a1cc6ca] FFTW v1.8.1
[9d29842c] FastAlmostBandedMatrices v0.1.4
[7034ab61] FastBroadcast v0.3.5
[9aa1b823] FastClosures v0.3.2
[442a2c76] FastGaussQuadrature v1.0.2
[a4df4552] FastPower v1.1.1
[fa42c844] FastRounding v0.3.1
[5789e2e9] FileIO v1.17.0
[8fc22ac5] FilePaths v0.8.3
[48062228] FilePathsBase v0.9.23
[1a297f60] FillArrays v1.13.0
[6a86dc24] FiniteDiff v2.27.0
[53c48c17] FixedPointNumbers v0.8.5
[1fa38f19] Format v1.3.7
[f6369f11] ForwardDiff v0.10.38
[5be70612] FrameTransformations v3.0.0
[b38be410] FreeType v4.1.1
[663a7486] FreeTypeAbstraction v0.10.6
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v0.1.3
[d9f16b24] Functors v0.5.2
[f7f18e0c] GLFW v3.4.3
[e9467ef8] GLMakie v0.11.3
[46192b85] GPUArraysCore v0.2.0
[c145ed77] GenericSchur v0.5.4
[68eda718] GeoFormatTypes v0.4.4
[cf35fbd7] GeoInterface v1.4.1
[5c1252a2] GeometryBasics v0.5.5
[a2bd30eb] Graphics v1.1.3
[86223c79] Graphs v1.12.0
[3955a311] GridLayoutBase v0.11.1
[42e2da0e] Grisu v1.0.2
[34004b35] HypergeometricFunctions v0.3.27
[4e86e20e] IERSConventions v1.1.2
[615f187c] IfElse v0.1.1
[2803e5a7] ImageAxes v0.6.12
[c817782e] ImageBase v0.1.7
[a09fc81d] ImageCore v0.10.5
[82e4d734] ImageIO v0.6.9
[6218d12a] ImageMagick v1.4.0
[bc367c6b] ImageMetadata v0.9.10
[9b13fd28] IndirectArrays v1.0.0
[d25df0c9] Inflate v0.1.5
[842dd82b] InlineStrings v1.4.3
[a98d9a8b] Interpolations v0.15.1
⌅ [d1acc4aa] IntervalArithmetic v0.20.9
[8197267c] IntervalSets v0.7.10
[3587e190] InverseFunctions v0.1.17
[41ab1584] InvertedIndices v1.3.1
[92d709cd] IrrationalConstants v0.2.4
[f1662d9f] Isoband v0.1.1
[c8e1da08] IterTools v1.10.0
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.7.0
[6b30ee2f] JSMDInterfaces v1.6.0
[67801824] JSMDUtils v1.2.1
[682c06a0] JSON v0.21.4
[0f8b85d8] JSON3 v1.14.1
[ae98c720] Jieko v0.2.1
[b835a17e] JpegTurbo v0.1.5
[4076af6c] JuMP v1.24.0
[ccbc3e58] JumpProcesses v9.14.2
[5ab0869b] KernelDensity v0.6.9
[ba0b0d4f] Krylov v0.9.10
[b964fa9f] LaTeXStrings v1.4.0
[10f19ff3] LayoutPointers v0.1.17
[5078a376] LazyArrays v2.6.1
[8cdb02fc] LazyModules v0.3.1
[2d8b4e74] LevyArea v1.0.0
[87fe0de2] LineSearch v0.1.4
[d3d80556] LineSearches v7.3.0
[7ed4a6bd] LinearSolve v3.3.1
[2ab3a3ac] LogExpFunctions v0.3.29
[4854310b] MINPACK v1.3.0
[1914dd2f] MacroTools v0.5.15
[ee78f7c6] Makie v0.22.2
[20f20a25] MakieCore v0.9.1
[d125e4d3] ManualMemory v0.1.8
[dbb5928d] MappedArrays v0.4.2
[b8f27783] MathOptInterface v1.37.0
[0a4f8689] MathTeXEngine v0.6.2
[a3b82374] MatrixFactorizations v3.0.1
[bb5d69b7] MaybeInplace v0.1.4
[7269a6da] MeshIO v0.5.2
[e1d29d7a] Missings v1.2.0
[66fc600b] ModernGL v1.1.8
[e94cdb99] MosaicViews v0.3.4
⌅ [6405355b] Mosek v10.2.0
[1ec41992] MosekTools v0.15.5
[2e0e35c7] Moshi v0.3.5
[46d2c3a1] MuladdMacro v0.2.4
[d8a4904e] MutableArithmetics v1.6.4
[d41bc354] NLSolversBase v7.8.3
[2774e3e8] NLsolve v4.5.1
[77ba4419] NaNMath v1.1.2
[f09324ee] Netpbm v1.1.1
[8913a72c] NonlinearSolve v4.4.0
[be0214bd] NonlinearSolveBase v1.5.0
[5959db7a] NonlinearSolveFirstOrder v1.3.0
[9a2c21bd] NonlinearSolveQuasiNewton v1.2.0
[26075421] NonlinearSolveSpectralMethods v1.1.0
[510215fc] Observables v0.5.5
[6fe1bfb0] OffsetArrays v1.15.0
[52e1d378] OpenEXR v0.3.3
[429524aa] Optim v1.11.0
[bac558e1] OrderedCollections v1.8.0
[1dea7af3] OrdinaryDiffEq v6.91.0
[89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.2.0
[6ad6398a] OrdinaryDiffEqBDF v1.2.0
[bbf590c4] OrdinaryDiffEqCore v1.18.1
[50262376] OrdinaryDiffEqDefault v1.3.0
[4302a76b] OrdinaryDiffEqDifferentiation v1.4.0
[9286f039] OrdinaryDiffEqExplicitRK v1.1.0
[e0540318] OrdinaryDiffEqExponentialRK v1.3.0
[becaefa8] OrdinaryDiffEqExtrapolation v1.4.0
[5960d6e9] OrdinaryDiffEqFIRK v1.7.0
[101fe9f7] OrdinaryDiffEqFeagin v1.1.0
[d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
[d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
[9f002381] OrdinaryDiffEqIMEXMultistep v1.2.0
[521117fe] OrdinaryDiffEqLinear v1.1.0
[1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
[b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
[127b3ac7] OrdinaryDiffEqNonlinearSolve v1.5.0
[c9986a66] OrdinaryDiffEqNordsieck v1.1.0
[5dd0a6cf] OrdinaryDiffEqPDIRK v1.2.0
[5b33eab2] OrdinaryDiffEqPRK v1.1.0
[04162be5] OrdinaryDiffEqQPRK v1.1.0
[af6ede74] OrdinaryDiffEqRKN v1.1.0
[43230ef6] OrdinaryDiffEqRosenbrock v1.6.0
[2d112036] OrdinaryDiffEqSDIRK v1.2.0
[669c94d9] OrdinaryDiffEqSSPRK v1.2.0
[e3e12d00] OrdinaryDiffEqStabilizedIRK v1.2.0
[358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
[fa646aed] OrdinaryDiffEqSymplecticRK v1.3.0
[b1df2697] OrdinaryDiffEqTsit5 v1.1.0
[79d7bb75] OrdinaryDiffEqVerner v1.1.1
[90014a1f] PDMats v0.11.32
[f57f5aa1] PNGFiles v0.4.4
[65ce6f38] PackageExtensionCompat v1.0.2
[19eb6ba3] Packing v0.5.1
[5432bcbf] PaddedViews v0.5.12
[d96e819e] Parameters v0.12.3
[69de0a69] Parsers v2.8.1
[eebad327] PkgVersion v0.3.3
[995b91a9] PlotUtils v1.4.3
[e409e4f3] PoissonRandom v0.4.4
[f517fe37] Polyester v0.7.16
[1d0040c9] PolyesterWeave v0.2.2
[647866c9] PolygonOps v0.1.2
[2dfb63ee] PooledArrays v1.4.3
[85a6dd25] PositiveFactorizations v0.2.4
[d236fae5] PreallocationTools v0.4.25
[aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.4.3
[08abe8d2] PrettyTables v2.4.0
[92933f4c] ProgressMeter v1.10.2
[43287f4e] PtrArrays v1.3.0
[4b34888f] QOI v1.0.1
[1fd47b50] QuadGK v2.11.2
[74087812] Random123 v1.7.0
[e6cf234a] RandomNumbers v1.6.0
[b3c3ace0] RangeArrays v0.3.2
[c84ed2f1] Ratios v0.4.5
[3cdcf5f2] RecipesBase v1.3.4
[731186ca] RecursiveArrayTools v3.31.0
[189a3867] Reexport v1.2.2
[74f56ac7] ReferenceFrameRotations v3.0.2
[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.0
[ae5879a3] ResettableStacks v1.1.1
[79098fc4] Rmath v0.8.0
[5eaf0fd0] RoundingEmulator v0.2.1
[7e49a35a] RuntimeGeneratedFunctions v0.5.13
[fdea26ae] SIMD v3.7.1
[94e857df] SIMDTypes v0.1.0
[b792745b] SMDGraphs v0.2.0
[0bca4576] SciMLBase v2.75.1
[19f34311] SciMLJacobianOperators v0.1.1
[c0aeaf25] SciMLOperators v0.3.12
[53ae85a6] SciMLStructures v1.6.1
[6c6a2e73] Scratch v1.2.1
[91c51154] SentinelArrays v1.4.8
[3cc68bcd] SetRounding v0.2.1
[efcf1570] Setfield v1.1.2
[65257c39] ShaderAbstractions v0.5.0
[992d4aef] Showoff v1.0.3
[73760f76] SignedDistanceFields v0.4.0
[727e6d20] SimpleNonlinearSolve v2.1.0
[699a6c99] SimpleTraits v0.9.4
[ce78b400] SimpleUnPack v1.1.0
[45858cf5] Sixel v0.1.3
[a2af1166] SortingAlgorithms v1.2.1
[47a9eef4] SparseDiffTools v2.23.1
[0a514795] SparseMatrixColorings v0.4.13
[276daf66] SpecialFunctions v2.5.0
[860ef19b] StableRNGs v1.0.2
[cae243ae] StackViews v0.1.1
[aedffcd0] Static v1.1.1
[0d7ed370] StaticArrayInterface v1.8.0
[90137ffa] StaticArrays v1.9.12
[1e83bf80] StaticArraysCore v1.4.3
[10745b16] Statistics v1.11.1
[82ae8749] StatsAPI v1.7.0
[2913bbd2] StatsBase v0.34.4
[4c63d2b9] StatsFuns v1.3.2
[9672c7b4] SteadyStateDiffEq v2.4.1
[789caeaf] StochasticDiffEq v6.74.0
[7792a7ef] StrideArraysCore v0.5.7
[69024149] StringEncodings v0.3.7
[892a3eda] StringManipulation v0.4.1
[09ab397b] StructArrays v0.7.0
[856f2bd8] StructTypes v1.11.0
[c3572dad] Sundials v4.26.1
[2efcf032] SymbolicIndexingInterface v0.3.38
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.12.0
[6aa5eb33] TaylorSeries v0.18.3
[c33777b2] Tempo v1.3.1
[62fd8b95] TensorCore v0.1.1
[8290d209] ThreadingUtilities v0.5.2
[731e570b] TiffImages v0.11.3
[a759f4b9] TimerOutputs v0.5.27
[3bb67fe8] TranscodingStreams v0.11.3
[981d1d27] TriplotBase v0.1.0
[781d530d] TruncatedStacktraces v1.4.0
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.22.0
[19fa3120] VertexSafeGraphs v0.2.0
[ea10d353] WeakRefStrings v1.4.2
[e3aaa7dc] WebP v0.1.3
[efce3f68] WoodburyMatrices v1.0.0
[76eceee3] WorkerUtilities v1.6.1
[ddb6d928] YAML v0.4.12
[6e34b625] Bzip2_jll v1.0.9+0
[4e9b3aee] CRlibm_jll v1.0.1+0
[83423d85] Cairo_jll v1.18.2+1
[ee1fde0b] Dbus_jll v1.14.10+0
[5ae413db] EarCut_jll v2.2.4+0
[2702e6a9] EpollShim_jll v0.0.20230411+1
[2e619515] Expat_jll v2.6.5+0
⌅ [b22a6f82] FFMPEG_jll v6.1.2+0
[f5851436] FFTW_jll v3.3.10+3
[a3f928ae] Fontconfig_jll v2.15.0+0
[d7e528f0] FreeType2_jll v2.13.3+1
[559328eb] FriBidi_jll v1.0.16+0
[0656b61e] GLFW_jll v3.4.0+2
[78b55507] Gettext_jll v0.21.0+0
[61579ee1] Ghostscript_jll v9.55.0+4
[59f7168a] Giflib_jll v5.2.3+0
[7746bdde] Glib_jll v2.82.4+0
[3b182d85] Graphite2_jll v1.3.14+1
[2e76f6c2] HarfBuzz_jll v8.5.0+0
[c73af94c] ImageMagick_jll v7.1.1+1
[905a6f67] Imath_jll v3.1.11+0
[1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
[aacddb02] JpegTurbo_jll v3.1.1+0
[c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
[1d63c593] LLVMOpenMP_jll v18.1.7+0
[dd4b983a] LZO_jll v2.10.3+0
⌅ [e9f186c6] Libffi_jll v3.2.2+2
[d4300ac3] Libgcrypt_jll v1.11.0+0
[7e76a0d4] Libglvnd_jll v1.7.0+0
[7add5ba3] Libgpg_error_jll v1.51.1+0
[94ce4f54] Libiconv_jll v1.18.0+0
[4b2f31a3] Libmount_jll v2.40.3+0
⌅ [89763e89] Libtiff_jll v4.4.0+0
[38a345b3] Libuuid_jll v2.40.3+0
⌃ [d3a379c0] LittleCMS_jll v2.12.0+0
[856f044c] MKL_jll v2025.0.1+1
[e7412a2a] Ogg_jll v1.3.5+1
[18a262bb] OpenEXR_jll v3.2.4+0
⌃ [643b3616] OpenJpeg_jll v2.4.0+0
[458c3c95] OpenSSL_jll v3.0.16+0
[efe28fd5] OpenSpecFun_jll v0.5.6+0
[91d4177d] Opus_jll v1.3.3+0
[36c8627f] Pango_jll v1.56.1+0
⌅ [30392449] Pixman_jll v0.43.4+0
[f50d1b31] Rmath_jll v0.5.1+0
⌅ [fb77eaff] Sundials_jll v5.2.3+0
[a2964d1f] Wayland_jll v1.21.0+2
[2381bf8a] Wayland_protocols_jll v1.36.0+0
[02c8fc9c] XML2_jll v2.13.6+1
[aed1982a] XSLT_jll v1.1.42+0
[4f6342f7] Xorg_libX11_jll v1.8.6+3
[0c0b7dd1] Xorg_libXau_jll v1.0.12+0
[935fb764] Xorg_libXcursor_jll v1.2.3+0
[a3789734] Xorg_libXdmcp_jll v1.1.5+0
[1082639a] Xorg_libXext_jll v1.3.6+3
[d091e8ba] Xorg_libXfixes_jll v6.0.0+0
[a51aa0fd] Xorg_libXi_jll v1.8.2+0
[d1454406] Xorg_libXinerama_jll v1.1.5+0
[ec84b674] Xorg_libXrandr_jll v1.5.4+0
[ea2f1a96] Xorg_libXrender_jll v0.9.11+1
[14d82f49] Xorg_libpthread_stubs_jll v0.1.2+0
[c7cfdc94] Xorg_libxcb_jll v1.17.0+3
[cc61e674] Xorg_libxkbfile_jll v1.1.2+1
[35661453] Xorg_xkbcomp_jll v1.4.6+1
[33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
[c5fb5394] Xorg_xtrans_jll v1.5.1+0
[3161d3a3] Zstd_jll v1.5.7+1
[b792d7bf] cminpack_jll v1.3.8+0
[9a68df92] isoband_jll v0.2.3+0
[a4ae2306] libaom_jll v3.11.0+0
[0ac62f75] libass_jll v0.15.2+0
[1183f4f0] libdecor_jll v0.2.2+0
[f638f0a6] libfdk_aac_jll v2.0.3+0
[b53b4c65] libpng_jll v1.6.46+0
[075b6546] libsixel_jll v1.10.5+0
[f27f6e37] libvorbis_jll v1.3.7+2
⌃ [c5f90fcd] libwebp_jll v1.4.0+0
[1317d2d5] oneTBB_jll v2022.0.0+0
[1270edf5] x264_jll v10164.0.1+0
⌅ [dfaa095f] x265_jll v3.6.0+0
[d8fb68d0] xkbcommon_jll v1.4.1+2
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[8bf52ea8] CRC32c v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.11.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.11.0
[de0858da] Printf v1.11.0
[9abbd945] Profile v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.11.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.6+0
[14a3606d] MozillaCACerts_jll v2023.12.12
[4536629a] OpenBLAS_jll v0.3.27+1
[05823500] OpenLibm_jll v0.8.1+2
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.7.0+0
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`- Output of
versioninfo()
Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 24 × 13th Gen Intel(R) Core(TM) i7-13700
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 24 virtual cores)
Environment:
JULIA_DEPOT_PATH = /workspace/julia
JULIA_EDITOR = code
JULIA_NUM_THREADS = Additional context
As you can see, the Gauss-Newton algorithm is perfectly capable to solve the problem, and it does so in much less iteration than Levenberg-Marquardt. However, the implementation in NonlinearSolve fails when specifying a sparse analytical Jacobian.