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Ring Modulator Work-Precision Diagrams

using OrdinaryDiffEq, DiffEqDevTools, Sundials, Plots, ODEInterfaceDiffEq, LSODA
using OrdinaryDiffEqBDF, OrdinaryDiffEqExponentialRK, OrdinaryDiffEqExtrapolation, OrdinaryDiffEqFIRK, OrdinaryDiffEqRosenbrock, OrdinaryDiffEqSDIRK, OrdinaryDiffEqStabilizedRK
using SciMLLogging
using LinearAlgebra, StaticArrays, RecursiveFactorization, Polyester, OrdinaryDiffEqCore
gr()

# Ring Modulator problem from the IVP Test Set
# Stiff system of 15 nonlinear ODEs from electrical circuit analysis
# Exact translation from Fortran feval subroutine at:
# http://archimede.dm.uniba.it/~testset/src/problems/ringmod.f

# Circuit parameters
const c_rm = 1.6e-8
const cs_rm = 2e-12
const cp_rm = 1e-8
const r_rm = 25e3
const rp_rm = 50.0
const lh_rm = 4.45
const ls1_rm = 2e-3
const ls2_rm = 5e-4
const ls3_rm = 5e-4
const rg1_rm = 36.3
const rg2_rm = 17.3
const rg3_rm = 17.3
const ri_rm = 50.0
const rc_rm = 600.0
const gamma_rm = 40.67286402e-9
const delta_rm = 17.7493332

function ringmod!(f, y, p, t)
    pi_val = 3.141592653589793238462643383

    uin1 = 0.5 * sin(2e3 * pi_val * t)
    uin2 = 2.0 * sin(2e4 * pi_val * t)
    ud1  = +y[3] - y[5] - y[7] - uin2
    ud2  = -y[4] + y[6] - y[7] - uin2
    ud3  = +y[4] + y[5] + y[7] + uin2
    ud4  = -y[3] - y[6] + y[7] + uin2

    qud1 = gamma_rm * (exp(delta_rm * ud1) - 1.0)
    qud2 = gamma_rm * (exp(delta_rm * ud2) - 1.0)
    qud3 = gamma_rm * (exp(delta_rm * ud3) - 1.0)
    qud4 = gamma_rm * (exp(delta_rm * ud4) - 1.0)

    f[1]  = (y[8] - 0.5*y[10] + 0.5*y[11] + y[14] - y[1]/r_rm) / c_rm
    f[2]  = (y[9] - 0.5*y[12] + 0.5*y[13] + y[15] - y[2]/r_rm) / c_rm
    f[3]  = (y[10] - qud1 + qud4) / cs_rm
    f[4]  = (-y[11] + qud2 - qud3) / cs_rm
    f[5]  = (y[12] + qud1 - qud3) / cs_rm
    f[6]  = (-y[13] - qud2 + qud4) / cs_rm
    f[7]  = (-y[7]/rp_rm + qud1 + qud2 - qud3 - qud4) / cp_rm
    f[8]  = -y[1] / lh_rm
    f[9]  = -y[2] / lh_rm
    f[10] = (0.5*y[1] - y[3] - rg2_rm*y[10]) / ls2_rm
    f[11] = (-0.5*y[1] + y[4] - rg3_rm*y[11]) / ls3_rm
    f[12] = (0.5*y[2] - y[5] - rg2_rm*y[12]) / ls2_rm
    f[13] = (-0.5*y[2] + y[6] - rg3_rm*y[13]) / ls3_rm
    f[14] = (-y[1] + uin1 - (ri_rm + rg1_rm)*y[14]) / ls1_rm
    f[15] = (-y[2] - (rc_rm + rg1_rm)*y[15]) / ls1_rm
end

u0 = zeros(15)
tspan = (0.0, 1e-3)

prob = ODEProblem{true, SciMLBase.FullSpecialize}(ringmod!, u0, tspan)

# Generate reference solution using tight tolerances
# This is a very oscillatory problem (10kHz forcing) requiring many steps
sol = solve(prob, CVODE_BDF(), abstol=1/10^14, reltol=1/10^14, maxiters=Int(1e7))
test_sol = TestSolution(sol)

abstols = 1.0 ./ 10.0 .^ (4:8)
reltols = 1.0 ./ 10.0 .^ (1:5);

The Ring Modulator describes an electrical circuit with diodes. The system has 15 variables: y[1]-y[2] are capacitor voltages, y[3]-y[7] involve diode voltages, y[8]-y[9] are inductor currents, and y[10]-y[15] are transformer currents. The forcing includes two sinusoidal inputs at 1kHz and 10kHz.

Reference plots from the IVP Test Set show oscillatory behavior in all components over [0, 1e-3]:

plot(sol, layout=(3,5), size=(1200,600), title=permutedims(["y$i" for i in 1:15]),
    legend=false, fmt=:png)

# Detailed view of first 4 components matching reference plots
p1 = plot(sol, idxs=[1], title="y(1)", legend=false)
p2 = plot(sol, idxs=[2], title="y(2)", legend=false)
p3 = plot(sol, idxs=[3], title="y(3)", legend=false)
p4 = plot(sol, idxs=[4], title="y(4)", legend=false)
plot(p1, p2, p3, p4, layout=(2,2), size=(800,600))

# Components y(5)-y(8) matching reference plots
p5 = plot(sol, idxs=[5], title="y(5)", legend=false)
p6 = plot(sol, idxs=[6], title="y(6)", legend=false)
p7 = plot(sol, idxs=[7], title="y(7)", legend=false)
p8 = plot(sol, idxs=[8], title="y(8)", legend=false)
plot(p5, p6, p7, p8, layout=(2,2), size=(800,600))

Omissions

The following were omitted from the tests due to convergence failures.

#sol = solve(prob,ROCK2()); # Unstable
#sol = solve(prob,ROCK4()); # Unstable
#sol = solve(prob,EXPRB53s3(),dt=2.0^(-20));
#sol = solve(prob,EPIRK4s3B(),dt=2.0^(-20));

High Tolerances

abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (1:4);
setups = [Dict(:alg=>Rosenbrock23()),
          Dict(:alg=>FBDF()),
          Dict(:alg=>QNDF()),
          Dict(:alg=>NordsieckBDF()),
          Dict(:alg=>TRBDF2()),
          Dict(:alg=>CVODE_BDF()),
          Dict(:alg=>radau()),
          Dict(:alg=>lsoda()),
          Dict(:alg=>RadauIIA5()),
          Dict(:alg=>ROS34PW1a()),
          ]
wp = WorkPrecisionSet(prob,abstols,reltols,setups;verbose=SciMLLogging.None(),
                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e6),numruns=10)
plot(wp)
EXIT OF RADAU AT X=        0.1118E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.1306E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.7058E-04
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.1170E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED

setups = [Dict(:alg=>Rosenbrock23()),
          Dict(:alg=>Kvaerno3()),
          Dict(:alg=>KenCarp4()),
          Dict(:alg=>TRBDF2()),
          Dict(:alg=>KenCarp3()),
          Dict(:alg=>lsoda()),
          Dict(:alg=>radau())]
names = ["Rosenbrock23" "Kvaerno3" "KenCarp4" "TRBDF2" "KenCarp3" "lsoda" "radau"]
wp = WorkPrecisionSet(prob,abstols,reltols,setups;names=names, verbose=SciMLLogging.None(),
                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e6),numruns=10)
plot(wp)
EXIT OF RADAU AT X=        0.1118E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.1306E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.7058E-04
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.1170E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED

setups = [Dict(:alg=>Rosenbrock23()),
          Dict(:alg=>TRBDF2()),
          Dict(:alg=>ImplicitEulerExtrapolation()),
          Dict(:alg=>ImplicitEulerBarycentricExtrapolation()),
          Dict(:alg=>ImplicitHairerWannerExtrapolation()),
          Dict(:alg=>FBDF()),
          Dict(:alg=>QNDF()),
          Dict(:alg=>NordsieckBDF()),
]
wp = WorkPrecisionSet(prob,abstols,reltols,setups; verbose=SciMLLogging.None(),
                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e6),numruns=10)
plot(wp)

Low Tolerances

This is the speed at lower tolerances, measuring what's good when accuracy is needed.

abstols = 1.0 ./ 10.0 .^ (7:12)
reltols = 1.0 ./ 10.0 .^ (4:9)

setups = [Dict(:alg=>FBDF()),
          Dict(:alg=>QNDF()),
          Dict(:alg=>NordsieckBDF()),
          Dict(:alg=>CVODE_BDF()),
          Dict(:alg=>ddebdf()),
          Dict(:alg=>Rodas4()),
          Dict(:alg=>Rodas5P()),
          Dict(:alg=>rodas()),
          Dict(:alg=>lsoda()),
          Dict(:alg=>radau()),
          Dict(:alg=>RadauIIA5()),
]
wp = WorkPrecisionSet(prob,abstols,reltols,setups;verbose=SciMLLogging.None(),
                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e6),numruns=10)
plot(wp)
EXIT OF RODAS AT X=        0.5900E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RODAS AT X=        0.1437E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.8449E-04
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.3258E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED

setups = [Dict(:alg=>Kvaerno4()),
          Dict(:alg=>Kvaerno5()),
          Dict(:alg=>CVODE_BDF()),
          Dict(:alg=>KenCarp4()),
          Dict(:alg=>KenCarp47()),
          Dict(:alg=>KenCarp5()),
          Dict(:alg=>Rodas4()),
          Dict(:alg=>Rodas5P()),
          Dict(:alg=>lsoda()),
          Dict(:alg=>radau()),
          Dict(:alg=>ImplicitEulerExtrapolation()),
          Dict(:alg=>ImplicitEulerBarycentricExtrapolation()),
          Dict(:alg=>ImplicitHairerWannerExtrapolation()),
          ]
wp = WorkPrecisionSet(prob,abstols,reltols,setups; verbose=SciMLLogging.None(),
                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e6),numruns=10)
plot(wp)
EXIT OF RADAU AT X=        0.8449E-04
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED
 EXIT OF RADAU AT X=        0.3258E-03
  MORE THAN NMAX =              1000000 STEPS ARE NEEDED

Multithreading benchmarks with Parallel Extrapolation Methods

#Setting BLAS to one thread to measure gains
LinearAlgebra.BLAS.set_num_threads(1)

abstols = 1.0 ./ 10.0 .^ (10:12)
reltols = 1.0 ./ 10.0 .^ (7:9)

setups = [
          Dict(:alg=>CVODE_BDF()),
          Dict(:alg=>KenCarp4()),
          Dict(:alg=>Rodas4()),
          Dict(:alg=>Rodas5P()),
          Dict(:alg=>QNDF()),
          Dict(:alg=>NordsieckBDF()),
          Dict(:alg=>lsoda()),
          Dict(:alg=>radau()),
          Dict(:alg=>seulex()),
          Dict(:alg=>ImplicitEulerExtrapolation(threading = OrdinaryDiffEqCore.PolyesterThreads())),
          Dict(:alg=>ImplicitEulerExtrapolation(threading = false)),
          Dict(:alg=>ImplicitEulerBarycentricExtrapolation(min_order = 4, threading = OrdinaryDiffEqCore.PolyesterThreads())),
          Dict(:alg=>ImplicitEulerBarycentricExtrapolation(min_order = 4, threading = false)),
          Dict(:alg=>ImplicitHairerWannerExtrapolation(threading = OrdinaryDiffEqCore.PolyesterThreads())),
          Dict(:alg=>ImplicitHairerWannerExtrapolation(threading = false)),
          ]

solnames = ["CVODE_BDF","KenCarp4","Rodas4","Rodas5P","QNDF","NordsieckBDF","lsoda","radau","seulex","ImplEulerExtpl (threaded)", "ImplEulerExtpl (non-threaded)",
           "ImplEulerBaryExtpl (threaded)","ImplEulerBaryExtpl (non-threaded)","ImplHWExtpl (threaded)","ImplHWExtpl (non-threaded)"]

wp = WorkPrecisionSet(prob,abstols,reltols,setups; verbose=SciMLLogging.None(),
                    names = solnames,save_everystep=false,appxsol=test_sol,maxiters=Int(1e6),numruns=10)

plot(wp, title = "Implicit Methods: Ring Modulator",legend=:outertopleft,size = (1000,500),
     xticks = 10.0 .^ (-15:1:1),
     yticks = 10.0 .^ (-6:0.3:5),
     bottom_margin= 5Plots.mm)

Conclusion

The Ring Modulator is a challenging 15-dimensional stiff ODE arising from electrical circuit analysis. At high tolerances, Rosenbrock23 and lsoda are fast. At lower tolerances, Rodas4, Rodas5P, and radau perform well. The problem features rapid oscillations from 1kHz and 10kHz forcing, making it a good test for stiff solvers.

Appendix

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/StiffODE","RingModulator.jmd")

Computer Information:

Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver2)
Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores)
Environment:
  JULIA_DEPOT_PATH = /home/crackauc/github-runners/amdci8-1/.julia
  JULIA_NUM_THREADS = auto

Package Information:

Status `~/github-runners/amdci8-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/StiffODE/Project.toml`
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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`

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  [7f56f5a3] LSODA v1.2.0
  [b964fa9f] LaTeXStrings v1.4.1
  [23fbe1c1] Latexify v0.16.12
  [10f19ff3] LayoutPointers v0.1.17
  [0e77f7df] LazilyInitializedFields v1.3.0
  [5078a376] LazyArrays v2.12.0
⌅ [1d6d02ad] LeftChildRightSiblingTrees v0.2.1
  [87fe0de2] LineSearch v0.1.16
⌃ [7ed4a6bd] LinearSolve v5.13.0
  [2ab3a3ac] LogExpFunctions v1.0.1
  [e6f89c97] LoggingExtras v1.2.0
  [bdcacae8] LoopVectorization v0.12.174
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [d0879d2d] MarkdownAST v0.1.3
  [a3b82374] MatrixFactorizations v3.1.3
  [bb5d69b7] MaybeInplace v0.1.8
  [739be429] MbedTLS v1.1.10
  [442fdcdd] Measures v0.3.3
⌅ [94925ecb] MethodOfLines v0.11.19
  [e1d29d7a] Missings v1.2.0
⌃ [961ee093] ModelingToolkit v11.39.1
⌃ [7771a370] ModelingToolkitBase v1.68.0
⌃ [6bb917b9] ModelingToolkitTearing v1.20.5
  [2e0e35c7] Moshi v0.3.12
  [46d2c3a1] MuladdMacro v0.2.7
  [102ac46a] MultivariatePolynomials v0.5.19
  [ffc61752] Mustache v1.0.21
  [d8a4904e] MutableArithmetics v1.8.0
  [77ba4419] NaNMath v1.1.4
⌃ [8913a72c] NonlinearSolve v4.28.0
⌃ [be0214bd] NonlinearSolveBase v2.47.0
⌃ [5959db7a] NonlinearSolveFirstOrder v2.4.0
⌃ [9a2c21bd] NonlinearSolveQuasiNewton v1.15.1
⌃ [26075421] NonlinearSolveSpectralMethods v1.8.0
  [54ca160b] ODEInterface v0.5.2
⌅ [09606e27] ODEInterfaceDiffEq v4.1.0
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.1
⌅ [bac558e1] OrderedCollections v1.8.2
⌃ [1dea7af3] OrdinaryDiffEq v7.7.0
⌃ [6ad6398a] OrdinaryDiffEqBDF v2.4.4
⌃ [bbf590c4] OrdinaryDiffEqCore v4.15.0
⌃ [50262376] OrdinaryDiffEqDefault v2.5.0
⌃ [4302a76b] OrdinaryDiffEqDifferentiation v3.10.0
⌃ [e0540318] OrdinaryDiffEqExponentialRK v2.3.0
⌃ [becaefa8] OrdinaryDiffEqExtrapolation v2.5.0
⌃ [5960d6e9] OrdinaryDiffEqFIRK v2.8.0
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.0
⌃ [5dd0a6cf] OrdinaryDiffEqPDIRK v2.4.0
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v2.7.0
⌃ [b4bd8bb3] OrdinaryDiffEqRosenbrockTableaus v2.4.1
⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.0
  [358294b1] OrdinaryDiffEqStabilizedRK v2.6.0
⌃ [b1df2697] OrdinaryDiffEqTsit5 v2.1.3
⌃ [79d7bb75] OrdinaryDiffEqVerner v2.4.0
⌃ [a7812802] PDEBase v0.1.33
  [90014a1f] PDMats v0.11.41
⌃ [65888b18] ParameterizedFunctions v5.26.0
⌅ [d96e819e] Parameters v0.12.3
⌅ [69de0a69] Parsers v2.8.7
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.7
  [e409e4f3] PoissonRandom v0.4.13
  [f517fe37] Polyester v0.7.19
  [1d0040c9] PolyesterWeave v0.2.2
⌃ [f27b6e38] Polynomials v4.1.1
⌃ [d236fae5] PreallocationTools v1.6.0
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.2
  [08abe8d2] PrettyTables v3.4.8
  [27ebfcd6] Primes v0.5.7
  [132c30aa] ProfileSVG v0.2.2
  [92933f4c] ProgressMeter v1.11.0
  [43287f4e] PtrArrays v1.4.0
  [78ab2635] PureGebal v1.1.0
  [0c0d3e7f] PureKLU v1.4.1
  [1fd47b50] QuadGK v2.11.3
⌅ [a08977f5] QuadratureRules v0.1.10
⌃ [c4ea9172] QuasiArrays v0.13.8
  [c84ed2f1] Ratios v0.4.5
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [807425ed] RecurrenceRelationships v0.2.0
⌃ [731186ca] RecursiveArrayTools v4.5.0
  [f2c3362d] RecursiveFactorization v0.2.30
  [189a3867] Reexport v1.2.2
  [2792f1a3] RegistryInstances v0.1.0
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.4.0
  [9fe22ead] RespecializeParams v1.3.0
  [79098fc4] Rmath v0.9.0
  [47965b36] RootedTrees v2.27.0
⌃ [f2b01f46] Roots v3.0.7
⌅ [fb486d5c] RungeKutta v0.5.23
  [7e49a35a] RuntimeGeneratedFunctions v0.5.25
⌃ [9dfe8606] SCCNonlinearSolve v1.15.0
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.46
  [1bc83da4] SafeTestsets v0.1.0
⌃ [0bca4576] SciMLBase v3.49.2
⌃ [31c91b34] SciMLBenchmarks v0.1.3
⌃ [19f34311] SciMLJacobianOperators v0.1.17
  [a6db7da4] SciMLLogging v2.1.0
⌃ [c0aeaf25] SciMLOperators v1.29.0
  [431bcebd] SciMLPublic v1.3.0
⌃ [53ae85a6] SciMLStructures v1.10.4
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
⌃ [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
⌃ [727e6d20] SimpleNonlinearSolve v2.14.0
⌅ [36b790f5] SimpleSolvers v0.9.2
  [699a6c99] SimpleTraits v0.9.6
  [a2af1166] SortingAlgorithms v1.2.3
  [bd59d7e1] SparseBandedMatrices v1.4.0
⌃ [a57abbd0] SparseColumnPivotedQR v2.1.7
⌃ [0a514795] SparseMatrixColorings v0.4.27
  [276daf66] SpecialFunctions v2.9.0
  [860ef19b] StableRNGs v1.0.4
  [0c0c59c1] StarAlgebras v0.3.0
⌃ [64909d44] StateSelection v1.11.0
  [aedffcd0] Static v1.4.6
  [0d7ed370] StaticArrayInterface v1.10.0
⌃ [90137ffa] StaticArrays v1.9.19
  [1e83bf80] StaticArraysCore v1.4.4
⌃ [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.13
  [4c63d2b9] StatsFuns v2.2.1
  [7792a7ef] StrideArraysCore v0.5.9
  [69024149] StringEncodings v0.3.7
⌅ [892a3eda] StringManipulation v0.5.0
  [09ab397b] StructArrays v0.7.3
  [c3572dad] Sundials v6.6.0
  [2efcf032] SymbolicIndexingInterface v0.3.55
⌃ [19f23fe9] SymbolicLimits v1.2.0
⌅ [d1185830] SymbolicUtils v4.45.0
⌃ [0c5d862f] Symbolics v7.36.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.14.0
  [ed4db957] TaskLocalValues v0.1.3
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [8290d209] ThreadingUtilities v0.5.6
⌅ [a759f4b9] TimerOutputs v0.5.29
  [c751599d] ToeplitzMatrices v0.8.5
  [3bb67fe8] TranscodingStreams v0.11.3
  [d5829a12] TriangularSolve v0.2.6
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.7.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.74
  [33b4df10] VectorizedRNG v0.2.26
  [81def892] VersionParsing v1.3.0
  [d30d5f5c] WeakCacheSets v0.1.0
  [44d3d7a6] Weave v0.10.12
  [efce3f68] WoodburyMatrices v1.1.0
  [ddb6d928] YAML v0.4.16
  [c2297ded] ZMQ v1.5.1
  [6e34b625] Bzip2_jll v1.0.9+0
  [83423d85] Cairo_jll v1.18.7+0
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.8.3+0
⌅ [b22a6f82] FFMPEG_jll v8.1.2+0
  [f5851436] FFTW_jll v3.3.12+0
  [34b6f7d7] FastTransforms_jll v0.6.4+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.14.3+1
  [559328eb] FriBidi_jll v1.0.17+0
⌃ [0656b61e] GLFW_jll v3.4.1+1
⌅ [d2c73de3] GR_jll v0.73.26+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [020c3dae] Git_LFS_jll v3.7.1+0
  [f8c6e375] Git_jll v2.55.0+0
  [7746bdde] Glib_jll v2.88.3+0
  [3b182d85] Graphite2_jll v1.3.16+0
⌅ [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.2.0+1
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.1.0+0
  [1d63c593] LLVMOpenMP_jll v22.1.7+0
  [aae0fff6] LSODA_jll v0.1.2+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.42.0+0
  [89763e89] Libtiff_jll v4.7.3+0
  [38a345b3] Libuuid_jll v2.42.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [c771fb93] ODEInterface_jll v0.0.2+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [656ef2d0] OpenBLAS32_jll v0.3.34+0
  [9bd350c2] OpenSSH_jll v10.5.1+0
⌃ [458c3c95] OpenSSL_jll v3.5.7+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
⌃ [36c8627f] Pango_jll v1.58.0+0
  [30392449] Pixman_jll v0.46.4+0
  [c0090381] Qt6Base_jll v6.10.2+2
  [629bc702] Qt6Declarative_jll v6.10.2+2
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [f50d1b31] Rmath_jll v0.5.2+0
⌃ [ca45d3f4] SuiteSparse32_jll v7.12.1+0
  [fb77eaff] Sundials_jll v7.5.0+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
  [ffd25f8a] XZ_jll v5.8.3+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.4+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [8f1865be] ZeroMQ_jll v4.3.6+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
  [a4ae2306] libaom_jll v3.14.1+0
⌃ [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [8e53e030] libdrm_jll v2.4.134+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.58+0
  [a9144af2] libsodium_jll v1.0.21+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [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
  [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
  [781609d7] GMP_jll v6.3.0+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [3a97d323] MPFR_jll v4.2.1+0
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [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`