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dgetrf: Singular matrix when solving a boundary value problem #830

@abhro

Description

@abhro

Describe the example

Starting with LinearSolve 3.46.0, the example taken from BoundaryValueDiffEq.jl's examples page fails: https://docs.sciml.ai/DiffEqDocs/stable/tutorials/bvp_example/#Example-3:-Semi-Explicit-Boundary-Value-Differential-Algebraic-Equations. It still produces results on v3.45.0, but that is the last working version.

Minimal Reproducible Example 👇

import BoundaryValueDiffEq as BVP
f(u, p, t) = [(1 + u[2] - sin(t)) * u[4] + cos(t),
              cos(t),
              u[4],
              (u[1] - sin(t)) * (u[4] - exp(t))]
bc(u, p, t) = [u[1], u[3] - 1, u[2] - sin(1.0)]
fun = BVP.BVPFunction(f, bc, mass_matrix = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 0])
prob = BVP.BVProblem(fun, zeros(4), (0.0, 1.0))
solver = BVP.Ascher4(; zeta = [0.0, 0.0, 1.0], jac_alg = BVP.BVPJacobianAlgorithm(BVP.AutoForwardDiff()))
sol = BVP.solve(prob, solver, dt = 0.01)

Error & Stacktrace ⚠️

┌ Error: BLAS/LAPACK dgetrf: Matrix is singular
│   Details: U(1,1) is exactly zero. The factorization has been completed, but U is singular and division by U will produce infinity.
│   Return code (info): 1
│   Matrix size: (303, 303)
│   Matrix type: Matrix{Float64}
│   Element type: Float64
│   Memory usage: 0.7 MB
│   RHS length: 303
│   RHS type: Vector{Float64}
└ @ LinearSolve ~/.julia/packages/LinearSolve/t9kBc/src/mkl.jl:273
ERROR: BLAS/LAPACK dgetrf: Matrix is singular
  Details: U(1,1) is exactly zero. The factorization has been completed, but U is singular and division by U will produce infinity.
  Return code (info): 1
  Matrix size: (303, 303)
  Matrix type: Matrix{Float64}
  Element type: Float64
  Memory usage: 0.7 MB
  RHS length: 303
  RHS type: Vector{Float64}
Stacktrace:
  [1] emit_message(message::String, level::Base.CoreLogging.LogLevel, file::String, line::Int64, _module::Module)
    @ SciMLLogging ~/.julia/packages/SciMLLogging/3uoc4/src/utils.jl:57
  [2] macro expansion
    @ ~/.julia/packages/SciMLLogging/3uoc4/src/utils.jl:147 [inlined]
  [3] solve!(cache::LinearSolve.LinearCache{…}, alg::LinearSolve.MKLLUFactorization; kwargs::@Kwargs{})
    @ LinearSolve ~/.julia/packages/LinearSolve/t9kBc/src/mkl.jl:273
  [4] solve!
    @ ~/.julia/packages/LinearSolve/t9kBc/src/mkl.jl:240 [inlined]
  [5] macro expansion
    @ ~/.julia/packages/LinearSolve/t9kBc/src/default.jl:514 [inlined]
  [6] solve!(::LinearSolve.LinearCache{…}, ::LinearSolve.DefaultLinearSolver; assump::LinearSolve.OperatorAssumptions{…}, kwargs::@Kwargs{})
    @ LinearSolve ~/.julia/packages/LinearSolve/t9kBc/src/default.jl:503
  [7] solve!
    @ ~/.julia/packages/LinearSolve/t9kBc/src/default.jl:503 [inlined]
  [8] #solve!#21
    @ ~/.julia/packages/LinearSolve/t9kBc/src/common.jl:441 [inlined]
  [9] solve!
    @ ~/.julia/packages/LinearSolve/t9kBc/src/common.jl:440 [inlined]
 [10] #_#1
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/ext/NonlinearSolveBaseLinearSolveExt.jl:24 [inlined]
 [11] LinearSolveJLCache
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/ext/NonlinearSolveBaseLinearSolveExt.jl:14 [inlined]
 [12] solve!(cache::NonlinearSolveBase.NewtonDescentCache{…}, J::Matrix{…}, fu::Vector{…}, u::Vector{…}, idx::Val{…}; skip_solve::Bool, new_jacobian::Bool, kwargs::@Kwargs{})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/mJsVc/src/descent/newton.jl:119
 [13] solve! (repeats 2 times)
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/descent/newton.jl:94 [inlined]
 [14] step!(cache::NonlinearSolveFirstOrder.GeneralizedFirstOrderAlgorithmCache{…}; recompute_jacobian::Nothing)
    @ NonlinearSolveFirstOrder ~/.julia/packages/NonlinearSolveFirstOrder/inFag/src/solve.jl:266
 [15] step!
    @ ~/.julia/packages/NonlinearSolveFirstOrder/inFag/src/solve.jl:244 [inlined]
 [16] #step!#180
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:559 [inlined]
 [17] step!
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:553 [inlined]
 [18] solve!(cache::NonlinearSolveFirstOrder.GeneralizedFirstOrderAlgorithmCache{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:287
 [19] #__solve#155
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:273 [inlined]
 [20] __solve
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:270 [inlined]
 [21] macro expansion
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:478 [inlined]
 [22] __generated_polysolve(::SciMLBase.NonlinearProblem{…}, ::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; stats::SciMLBase.NLStats, alias::SciMLBase.NonlinearAliasSpecifier, verbose::NonlinearSolveBase.NonlinearVerbosity{…}, initializealg::NonlinearSolveBase.NonlinearSolveDefaultInit, kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:423
 [23] __generated_polysolve
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:423 [inlined]
 [24] #__solve#166
    @ ~/.julia/packages/NonlinearSolveBase/mJsVc/src/solve.jl:396 [inlined]
 [25] __perform_ascher_iteration(cache::BoundaryValueDiffEqAscher.AscherCache{…}, abstol::Float64, adaptive::Bool)
    @ BoundaryValueDiffEqAscher ~/.julia/packages/BoundaryValueDiffEqAscher/CPeel/src/ascher.jl:180
 [26] solve!(cache::BoundaryValueDiffEqAscher.AscherCache{…})
    @ BoundaryValueDiffEqAscher ~/.julia/packages/BoundaryValueDiffEqAscher/CPeel/src/ascher.jl:162
 [27] #__solve#34
    @ ~/.julia/packages/BoundaryValueDiffEqCore/hFduL/src/BoundaryValueDiffEqCore.jl:38 [inlined]
 [28] __solve
    @ ~/.julia/packages/BoundaryValueDiffEqCore/hFduL/src/BoundaryValueDiffEqCore.jl:35 [inlined]
 [29] #solve_call#24
    @ ~/.julia/packages/DiffEqBase/6sydR/src/solve.jl:142 [inlined]
 [30] solve_call
    @ ~/.julia/packages/DiffEqBase/6sydR/src/solve.jl:109 [inlined]
 [31] solve_up(prob::SciMLBase.BVProblem{…}, sensealg::Nothing, u0::Vector{…}, p::SciMLBase.NullParameters, args::BoundaryValueDiffEqAscher.Ascher4{…}; originator::SciMLBase.ChainRulesOriginator, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/6sydR/src/solve.jl:578
 [32] solve_up
    @ ~/.julia/packages/DiffEqBase/6sydR/src/solve.jl:555 [inlined]
 [33] #solve#30
    @ ~/.julia/packages/DiffEqBase/6sydR/src/solve.jl:545 [inlined]
 [34] top-level scope
    @ REPL[8]:1
Some type information was truncated. Use `show(err)` to see complete types.

Not Working Environment (please complete the following information):

  • Output of using Pkg; Pkg.status()
Status `~/.julia/environments/bvp-mwe/Project.toml`
  [764a87c0] BoundaryValueDiffEq v5.18.0
  [7ed4a6bd] LinearSolve v3.47.0
  • Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/.julia/environments/bvp-mwe/Manifest.toml`
  [47edcb42] ADTypes v1.19.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.4.0
  [a95523ee] AlmostBlockDiagonals v0.1.10
  [4fba245c] ArrayInterface v7.22.0
  [4c555306] ArrayLayouts v1.12.1
  [aae01518] BandedMatrices v1.10.2
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.18.0
  [7227322d] BoundaryValueDiffEqAscher v1.8.0
  [56b672f2] BoundaryValueDiffEqCore v1.11.1
  [85d9eb09] BoundaryValueDiffEqFIRK v1.9.0
  [1a22d4ce] BoundaryValueDiffEqMIRK v1.9.0
  [9255f1d6] BoundaryValueDiffEqMIRKN v1.8.0
  [ed55bfe0] BoundaryValueDiffEqShooting v1.9.0
  [2a0fbf3d] CPUSummary v0.2.7
  [d360d2e6] ChainRulesCore v1.26.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.18.1
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.6.0
  [adafc99b] CpuId v0.3.1
  [2b5f629d] DiffEqBase v6.192.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.12
  [ffbed154] DocStringExtensions v0.9.5
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.17
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [9d29842c] FastAlmostBandedMatrices v0.1.5
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.2.0
  [1a297f60] FillArrays v1.15.0
  [6a86dc24] FiniteDiff v2.29.0
  [f6369f11] ForwardDiff v1.3.0
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [615f187c] IfElse v0.1.1
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.1
  [ae98c720] Jieko v0.2.1
  [ba0b0d4f] Krylov v0.10.2
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.9.1
  [87fe0de2] LineSearch v0.1.4
  [7ed4a6bd] LinearSolve v3.47.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [a3b82374] MatrixFactorizations v3.1.3
  [bb5d69b7] MaybeInplace v0.1.4
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
  [77ba4419] NaNMath v1.1.3
  [be0214bd] NonlinearSolveBase v2.4.0
  [5959db7a] NonlinearSolveFirstOrder v1.10.0
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
  [d236fae5] PreallocationTools v0.4.34
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.39.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.16
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.127.0
  [19f34311] SciMLJacobianOperators v0.1.11
  [a6db7da4] SciMLLogging v1.5.0
  [c0aeaf25] SciMLOperators v1.13.0
  [431bcebd] SciMLPublic v1.0.0
  [53ae85a6] SciMLStructures v1.7.0
  [efcf1570] Setfield v1.1.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [aedffcd0] Static v1.3.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [7792a7ef] StrideArraysCore v0.5.8
  [2efcf032] SymbolicIndexingInterface v0.3.46
  [8290d209] ThreadingUtilities v0.5.5
  [a759f4b9] TimerOutputs v0.5.29
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 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
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.0
  [de0858da] Printf v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
  [deac9b47] LibCURL_jll v8.11.1+1
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.5.20
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.1+0
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.5.0+2
  • Output of versioninfo()
Julia Version 1.12.1
Commit ba1e628ee49 (2025-10-17 13:02 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × 13th Gen Intel(R) Core(TM) i5-1340P
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, alderlake)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 16 virtual cores)

Working Environment (please complete the following information):

  • Output of using Pkg; Pkg.status()
Status `~/.julia/environments/bvp-mwe-working/Project.toml`
  [764a87c0] BoundaryValueDiffEq v5.18.0
⌃ [7ed4a6bd] LinearSolve v3.45.0
Info Packages marked with ⌃ have new versions available and may be upgradable.
  • Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/.julia/environments/bvp-mwe-working/Manifest.toml`
  [47edcb42] ADTypes v1.19.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.4.0
  [a95523ee] AlmostBlockDiagonals v0.1.10
  [4fba245c] ArrayInterface v7.22.0
  [4c555306] ArrayLayouts v1.12.1
  [aae01518] BandedMatrices v1.10.2
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.18.0
  [7227322d] BoundaryValueDiffEqAscher v1.8.0
  [56b672f2] BoundaryValueDiffEqCore v1.11.1
  [85d9eb09] BoundaryValueDiffEqFIRK v1.9.0
  [1a22d4ce] BoundaryValueDiffEqMIRK v1.9.0
  [9255f1d6] BoundaryValueDiffEqMIRKN v1.8.0
  [ed55bfe0] BoundaryValueDiffEqShooting v1.9.0
  [2a0fbf3d] CPUSummary v0.2.7
  [d360d2e6] ChainRulesCore v1.26.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.18.1
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.6.0
  [adafc99b] CpuId v0.3.1
  [2b5f629d] DiffEqBase v6.192.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.12
  [ffbed154] DocStringExtensions v0.9.5
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.17
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [9d29842c] FastAlmostBandedMatrices v0.1.5
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.2.0
  [1a297f60] FillArrays v1.15.0
  [6a86dc24] FiniteDiff v2.29.0
  [f6369f11] ForwardDiff v1.3.0
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [615f187c] IfElse v0.1.1
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.1
  [ae98c720] Jieko v0.2.1
  [ba0b0d4f] Krylov v0.10.2
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.9.1
  [87fe0de2] LineSearch v0.1.4
⌃ [7ed4a6bd] LinearSolve v3.45.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [a3b82374] MatrixFactorizations v3.1.3
  [bb5d69b7] MaybeInplace v0.1.4
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
  [77ba4419] NaNMath v1.1.3
⌃ [be0214bd] NonlinearSolveBase v2.0.0
⌃ [5959db7a] NonlinearSolveFirstOrder v1.9.0
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
  [d236fae5] PreallocationTools v0.4.34
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.39.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.16
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.127.0
  [19f34311] SciMLJacobianOperators v0.1.11
  [a6db7da4] SciMLLogging v1.5.0
  [c0aeaf25] SciMLOperators v1.13.0
  [431bcebd] SciMLPublic v1.0.0
  [53ae85a6] SciMLStructures v1.7.0
  [efcf1570] Setfield v1.1.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [aedffcd0] Static v1.3.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [7792a7ef] StrideArraysCore v0.5.8
  [2efcf032] SymbolicIndexingInterface v0.3.46
  [8290d209] ThreadingUtilities v0.5.5
  [a759f4b9] TimerOutputs v0.5.29
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 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
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.0
  [de0858da] Printf v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
  [deac9b47] LibCURL_jll v8.11.1+1
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.5.20
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.1+0
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.5.0+2
Info Packages marked with ⌃ have new versions available and may be upgradable.
  • Output of versioninfo()
Julia Version 1.12.1
Commit ba1e628ee49 (2025-10-17 13:02 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × 13th Gen Intel(R) Core(TM) i5-1340P
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, alderlake)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 16 virtual cores)

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