Beam Work-Precision Diagrams
using OrdinaryDiffEq, DiffEqDevTools, Sundials, Plots, ODEInterfaceDiffEq, LSODA
using OrdinaryDiffEqBDF, OrdinaryDiffEqExtrapolation, OrdinaryDiffEqFIRK, OrdinaryDiffEqRosenbrock, OrdinaryDiffEqSDIRK, OrdinaryDiffEqStabilizedRK
using SciMLLogging
using LinearAlgebra, RecursiveFactorization, Polyester, PreallocationTools, OrdinaryDiffEqCore
gr()
# Beam problem from the IVP Test Set
# ODE of dimension 80 (N=40 discretization points, 2*N unknowns)
# Describes the deformation of a beam under an applied force
# Exact translation from Fortran feval subroutine at:
# http://archimede.dm.uniba.it/~testset/src/problems/beam.f
const N_beam = 40
const NN_beam = 2 * N_beam
const NSQ_beam = N_beam * N_beam
const NQUATR_beam = NSQ_beam * NSQ_beam
const DELTAS_beam = 1.0 / N_beam
# Pre-allocate work buffers using DiffCache for ForwardDiff compatibility
const _beam_sth = DiffCache(zeros(N_beam))
const _beam_cth = DiffCache(zeros(N_beam))
const _beam_v = DiffCache(zeros(N_beam))
const _beam_w = DiffCache(zeros(N_beam))
const _beam_alpha = DiffCache(zeros(N_beam))
const _beam_beta = DiffCache(zeros(N_beam))
const _beam_u = DiffCache(zeros(N_beam))
function beam!(df, th, p, t)
N = N_beam
NN = NN_beam
sth = get_tmp(_beam_sth, df)
cth = get_tmp(_beam_cth, df)
v = get_tmp(_beam_v, df)
w = get_tmp(_beam_w, df)
alpha = get_tmp(_beam_alpha, df)
beta = get_tmp(_beam_beta, df)
u = get_tmp(_beam_u, df)
# Precompute sin and cos of differences (indices 2:N only)
for i in 2:N
thdiff = th[i] - th[i-1]
sth[i] = sin(thdiff)
cth[i] = cos(thdiff)
end
# Compute right-hand side of the linear system
if t > pi
# Case t > pi: no external force
v[1] = (-3.0*th[1] + th[2]) * NQUATR_beam
for i in 2:N-1
v[i] = (th[i-1] - 2.0*th[i] + th[i+1]) * NQUATR_beam
end
v[N] = (th[N-1] - th[N]) * NQUATR_beam
else
# Case t <= pi: with applied force
fabs = 1.5 * sin(t)^2
fx = -fabs
fy = fabs
v[1] = (-3.0*th[1] + th[2]) * NQUATR_beam +
NSQ_beam * (fy*cos(th[1]) - fx*sin(th[1]))
for i in 2:N-1
v[i] = (th[i-1] - 2.0*th[i] + th[i+1]) * NQUATR_beam +
NSQ_beam * (fy*cos(th[i]) - fx*sin(th[i]))
end
v[N] = (th[N-1] - th[N]) * NQUATR_beam +
NSQ_beam * (fy*cos(th[N]) - fx*sin(th[N]))
end
# Compute product DV = W
w[1] = sth[2] * v[2]
for i in 2:N-1
w[i] = -sth[i]*v[i-1] + sth[i+1]*v[i+1]
end
w[N] = -sth[N] * v[N-1]
# Add term 3: w[i] += th[N+i]^2
for i in 1:N
w[i] += th[N+i]^2
end
# Solve tridiagonal system CW = W
alpha[1] = 1.0
for i in 2:N
alpha[i] = 2.0
beta[i-1] = -cth[i]
end
alpha[N] = 3.0
# Forward elimination
for i in N-1:-1:1
q = beta[i] / alpha[i+1]
w[i] = w[i] - w[i+1] * q
alpha[i] = alpha[i] - beta[i] * q
end
# Back substitution
w[1] = w[1] / alpha[1]
for i in 2:N
w[i] = (w[i] - beta[i-1]*w[i-1]) / alpha[i]
end
# Compute U = CV + DW
u[1] = v[1] - cth[2]*v[2] + sth[2]*w[2]
for i in 2:N-1
u[i] = 2.0*v[i] - cth[i]*v[i-1] - cth[i+1]*v[i+1] -
sth[i]*w[i-1] + sth[i+1]*w[i+1]
end
u[N] = 3.0*v[N] - cth[N]*v[N-1] - sth[N]*w[N-1]
# Put derivatives in right place
for i in 1:N
df[i] = th[N+i] # theta' = omega
df[N+i] = u[i] # omega' = u
end
end
u0 = zeros(NN_beam)
tspan = (0.0, 5.0)
prob = ODEProblem{true, SciMLBase.FullSpecialize}(beam!, u0, tspan)
# Generate reference solution using tight tolerances
# The beam problem is moderately stiff and needs 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 .^ (4:11)
reltols = 1.0 ./ 10.0 .^ (1:8);The Beam problem describes the dynamics of a flexible beam under an applied force. The beam is discretized into N=40 segments, giving 80 ODEs (40 angles + 40 angular velocities). The force is applied for t ∈ [0, π] and then released, causing the beam to oscillate.
Reference plots from the IVP Test Set show the angular velocities z(10), z(20), z(30), z(40) (components 50, 60, 70, 80) peaking around t=1-2 and oscillating:
# Plot angular velocities matching reference: z(10)=y(50), z(20)=y(60), z(30)=y(70), z(40)=y(80)
p1 = plot(sol, idxs=[50], title="z(10)", legend=false)
p2 = plot(sol, idxs=[60], title="z(20)", legend=false)
p3 = plot(sol, idxs=[70], title="z(30)", legend=false)
p4 = plot(sol, idxs=[80], title="z(40)", legend=false)
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# Plot angles: y(10), y(20), y(30), y(40)
p1 = plot(sol, idxs=[10], title="y(10)", legend=false)
p2 = plot(sol, idxs=[20], title="y(20)", legend=false)
p3 = plot(sol, idxs=[30], title="y(30)", legend=false)
p4 = plot(sol, idxs=[40], title="y(40)", legend=false)
plot(p1, p2, p3, p4, 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()); # UnstableHigh 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=>rodas()),
Dict(:alg=>radau()),
Dict(:alg=>lsoda()),
Dict(:alg=>RadauIIA5()),
]
wp = WorkPrecisionSet(prob,abstols,reltols,setups;verbose=SciMLLogging.None(),
save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=10)
plot(wp)
setups = [Dict(:alg=>Rosenbrock23()),
Dict(:alg=>Kvaerno3()),
Dict(:alg=>CVODE_BDF()),
Dict(:alg=>KenCarp4()),
Dict(:alg=>TRBDF2()),
Dict(:alg=>KenCarp3()),
Dict(:alg=>Rodas4()),
Dict(:alg=>lsoda()),
Dict(:alg=>radau())]
wp = WorkPrecisionSet(prob,abstols,reltols,setups; verbose=SciMLLogging.None(),
save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=10)
plot(wp)
setups = [Dict(:alg=>Rosenbrock23()),
Dict(:alg=>TRBDF2()),
Dict(:alg=>ImplicitEulerExtrapolation()),
Dict(:alg=>ImplicitEulerBarycentricExtrapolation()),
Dict(:alg=>ImplicitHairerWannerExtrapolation()),
Dict(:alg=>ABDF2()),
Dict(:alg=>FBDF()),
Dict(:alg=>NordsieckBDF()),
]
wp = WorkPrecisionSet(prob,abstols,reltols,setups; verbose=SciMLLogging.None(),
save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),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=>radau()),
Dict(:alg=>lsoda()),
]
wp = WorkPrecisionSet(prob,abstols,reltols,setups;verbose=SciMLLogging.None(),
save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=10)
plot(wp)EXIT OF RODAS AT X= 0.2879E+01
MORE THAN NMAX = 100000 STEPS ARE NEEDED
setups = [Dict(:alg=>Kvaerno4()),
Dict(:alg=>Kvaerno5()),
Dict(:alg=>CVODE_BDF()),
Dict(:alg=>KenCarp4()),
Dict(:alg=>KenCarp5()),
Dict(:alg=>Rodas4()),
Dict(:alg=>Rodas5P()),
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(1e5),numruns=10)
plot(wp)
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(1e5),numruns=10)
plot(wp, title = "Implicit Methods: Beam",legend=:outertopleft,size = (1000,500),
xticks = 10.0 .^ (-15:1:1),
yticks = 10.0 .^ (-6:0.3:5),
bottom_margin= 5Plots.mm)
Conclusion
The Beam problem is an 80-dimensional stiff ODE from structural mechanics. It involves solving a tridiagonal system at each RHS evaluation, which adds computational cost per function evaluation. CVODE_BDF and Rodas4/Rodas5P perform well across tolerance ranges. The implicit extrapolation methods benefit from multithreading on this larger problem.
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","Beam.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: 1 default, 0 interactive, 1 GC (on 128 virtual cores)
Environment:
JULIA_PKG_PRECOMPILE_AUTO = 0
Package Information:
Status `~/sandbox/tmp_20260825_180339_53321/stiffode-master-full/benchmarks/StiffODE/Project.toml`
[2169fc97] AlgebraicMultigrid v2.0.1
[6e4b80f9] BenchmarkTools v1.8.0
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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`And the full manifest:
Status `~/sandbox/tmp_20260825_180339_53321/stiffode-master-full/benchmarks/StiffODE/Manifest.toml`
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[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`