Lotka-Volterra Work-Precision Diagrams

Lotka-Volterra

The purpose of this problem is to test the performance on easy problems. Since it's periodic, the error is naturally low, and so most of the difference will come down to startup times and, when measuring the interpolations, the algorithm choices.

using OrdinaryDiffEq, ParameterizedFunctions, ODEInterfaceDiffEq, LSODA,
      Sundials, DiffEqDevTools, StaticArrays

f = @ode_def LotkaVolterra begin
  dx = a*x - b*x*y
  dy = -c*y + d*x*y
end a b c d

p = SA[1.5,1.0,3.0,1.0]
prob = ODEProblem{true, SciMLBase.FullSpecialize}(f,[1.0;1.0],(0.0,10.0),p)
probstatic = ODEProblem{false}(f,SA[1.0;1.0],(0.0,10.0),p)

abstols = 1.0 ./ 10.0 .^ (6:13)
reltols = 1.0 ./ 10.0 .^ (3:10);
sol = solve(prob,Vern7(),abstol=1/10^14,reltol=1/10^14)
sol2 = solve(probstatic,Vern7(),abstol=1/10^14,reltol=1/10^14)
probs = [prob,probstatic]
test_sol = [sol,sol2];
using Plots; gr()

Plots.GRBackend()

plot(sol)

Low Order

setups = [Dict(:alg=>DP5())
          #Dict(:alg=>ode45()) # fail
          Dict(:alg=>dopri5())
          Dict(:alg=>Tsit5())
          Dict(:alg=>Vern6())
          Dict(:alg=>Tsit5(), :prob_choice => 2)
          Dict(:alg=>Vern6(), :prob_choice => 2)
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,save_everystep=false,maxiters=10000,numruns=100)
plot(wp)

Here we see the OrdinaryDiffEq.jl algorithms once again far in the lead.

Interpolation Error

Since the problem is periodic, the real measure of error is the error throughout the solution.

setups = [Dict(:alg=>DP5())
          #Dict(:alg=>ode45())
          Dict(:alg=>Tsit5())
          Dict(:alg=>Vern6())
          Dict(:alg=>Tsit5(), :prob_choice => 2)
          Dict(:alg=>Vern6(), :prob_choice => 2)
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,maxiters=10000,error_estimate=:L2,dense_errors=true,numruns=100)
plot(wp)

Here we see the power of algorithm specific interpolations. The ODE.jl algorithm is only able to reach $10^{-7}$ error even at a tolerance of $10^{-13}$, while the DifferentialEquations.jl algorithms are below $10^{-10}$

Higher Order

setups = [Dict(:alg=>DP8())
          Dict(:alg=>dop853())
          #Dict(:alg=>ode78()) # fails
          Dict(:alg=>Vern6())
          Dict(:alg=>Vern7())
          Dict(:alg=>Vern8())
          Dict(:alg=>Vern9())
          Dict(:alg=>Vern6(), :prob_choice => 2)
          Dict(:alg=>Vern7(), :prob_choice => 2)
          Dict(:alg=>Vern8(), :prob_choice => 2)
          Dict(:alg=>Vern9(), :prob_choice => 2)
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,save_everystep=false,maxiters=1000,numruns=100)
plot(wp)

setups = [Dict(:alg=>odex())
          Dict(:alg=>ddeabm())
          Dict(:alg=>Vern6())
          Dict(:alg=>Vern7())
          Dict(:alg=>Vern8())
          Dict(:alg=>Vern9())
          Dict(:alg=>Vern6(), :prob_choice => 2)
          Dict(:alg=>Vern7(), :prob_choice => 2)
          Dict(:alg=>Vern8(), :prob_choice => 2)
          Dict(:alg=>Vern9(), :prob_choice => 2)
          Dict(:alg=>CVODE_Adams())
          Dict(:alg=>lsoda())
          Dict(:alg=>ARKODE(Sundials.Explicit(),order=6))
          ]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,save_everystep=false,maxiters=1000,numruns=100)
plot(wp)

Again we look at interpolations:

setups = [Dict(:alg=>DP8())
          #Dict(:alg=>ode78())
          Dict(:alg=>Vern6())
          Dict(:alg=>Vern7())
          Dict(:alg=>Vern8())
          Dict(:alg=>Vern9())
          Dict(:alg=>Vern6(), :prob_choice => 2)
          Dict(:alg=>Vern7(), :prob_choice => 2)
          Dict(:alg=>Vern8(), :prob_choice => 2)
          Dict(:alg=>Vern9(), :prob_choice => 2)
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,dense=true,maxiters=1000,error_estimate=:L2,numruns=100)
plot(wp)

Again, the ODE.jl algorithms suffer when measuring the interpolations due to relying on an order 3 Hermite polynomial instead of an algorithm-specific order matching interpolation which uses the timesteps.

Comparison with Non-RK methods

Now let's test Tsit5 and Vern9 against parallel extrapolation methods and an Adams-Bashforth-Moulton:

abstols = 1.0 ./ 10.0 .^ (8:13)
reltols = 1.0 ./ 10.0 .^ (8:13)
setups = [Dict(:alg=>Tsit5())
          Dict(:alg=>Vern9())
          Dict(:alg=>VCABM())
          Dict(:alg=>Vern9(), :prob_choice => 2)
          Dict(:alg=>VCABM(), :prob_choice => 2)
          Dict(:alg=>AitkenNeville(min_order=1, max_order=9, init_order=4, threading=true))
          Dict(:alg=>ExtrapolationMidpointDeuflhard(min_order=1, max_order=9, init_order=4, threading=true))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=11, init_order=4, threading=true))]
solnames = ["Tsit5","Vern9","VCABM","Vern9 Static","VCABM Static","AitkenNeville","Midpoint Deuflhard","Midpoint Hairer Wanner"]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,names=solnames,
                      save_everystep=false,verbose=false,numruns=100)
plot(wp)

setups = [Dict(:alg=>ExtrapolationMidpointDeuflhard(min_order=1, max_order=9, init_order=9, threading=false))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=11, init_order=4, threading=false))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=11, init_order=4, threading=true))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=11, init_order=4, sequence = :romberg, threading=true))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=11, init_order=4, sequence = :bulirsch, threading=true))]
solnames = ["Deuflhard","No threads","standard","Romberg","Bulirsch"]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,names=solnames,
                      save_everystep=false,verbose=false,numruns=100)
plot(wp)

setups = [Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=11, init_order=10, threading=true))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=11, init_order=4, threading=true))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=5, max_order=11, init_order=10, threading=true))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=2, max_order=15, init_order=10, threading=true))
          Dict(:alg=>ExtrapolationMidpointHairerWanner(min_order=5, max_order=7, init_order=6, threading=true))]
solnames = ["1","2","3","4","5"]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;appxsol=test_sol,names=solnames,
                      save_everystep=false,verbose=false,numruns=100)
plot(wp)

Conclusion

The OrdinaryDiffEq.jl are quicker and still solve to a much higher accuracy, especially when the interpolations are involved. ODE.jl errors a lot.

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/NonStiffODE","LotkaVolterra_wpd.jmd")

Computer Information:

Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 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
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores)
Environment:
  JULIA_CPU_THREADS = 128
  JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953

Package Information:

Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonStiffODE/Project.toml`
  [f3b72e0c] DiffEqDevTools v2.44.4
  [7f56f5a3] LSODA v0.7.5
  [54ca160b] ODEInterface v0.5.0
  [09606e27] ODEInterfaceDiffEq v3.13.3
  [1dea7af3] OrdinaryDiffEq v6.87.0
  [65888b18] ParameterizedFunctions v5.17.0
  [91a5bcdd] Plots v1.40.5
  [31c91b34] SciMLBenchmarks v0.1.3
  [90137ffa] StaticArrays v1.9.7
  [c3572dad] Sundials v4.24.0
  [9a3f8284] Random

And the full manifest:

Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonStiffODE/Manifest.toml`
  [47edcb42] ADTypes v1.6.1
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.37
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.12.0
  [4c555306] ArrayLayouts v1.10.2
  [e2ed5e7c] Bijections v0.1.7
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [49dc2e85] Calculus v0.5.1
  [d360d2e6] ChainRulesCore v1.24.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [944b1d66] CodecZlib v0.7.5
  [35d6a980] ColorSchemes v3.26.0
  [3da002f7] ColorTypes v0.11.5
  [c3611d14] ColorVectorSpace v0.10.0
  [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.15.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
  [8f4d0f93] Conda v1.10.2
  [187b0558] ConstructionBase v1.5.6
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.151.5
  [459566f4] DiffEqCallbacks v3.6.2
  [f3b72e0c] DiffEqDevTools v2.44.4
  [77a26b50] DiffEqNoiseProcess v5.22.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.5.9
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.109
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [fa6b7ba4] DualNumbers v0.6.8
⌅ [7c1d4256] DynamicPolynomials v0.5.7
⌅ [06fc5a27] DynamicQuantities v0.13.2
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.7.7
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [c87230d0] FFMPEG v0.4.1
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [1a297f60] FillArrays v1.11.0
  [64ca27bc] FindFirstFunctions v1.2.0
  [6a86dc24] FiniteDiff v2.23.1
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.11
  [46192b85] GPUArraysCore v0.1.6
  [28b8d3ca] GR v0.73.7
  [c145ed77] GenericSchur v0.5.4
  [d7ba0133] Git v1.3.1
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.11.2
  [42e2da0e] Grisu v1.0.2
  [cd3eb016] HTTP v1.10.8
  [eafb193a] Highlights v0.5.3
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.23
  [7073ff75] IJulia v1.25.0
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.15
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.7
  [692b3bcd] JLLWrappers v1.5.0
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.59
  [ccbc3e58] JumpProcesses v9.12.0
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.6
  [7f56f5a3] LSODA v0.7.5
  [b964fa9f] LaTeXStrings v1.3.1
  [2ee39098] LabelledArrays v1.16.0
  [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.4
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.1.9
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.30.2
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.0.3
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.3
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.26.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.6
  [ffc61752] Mustache v1.0.19
  [d8a4904e] MutableArithmetics v1.4.5
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.13.1
  [54ca160b] ODEInterface v0.5.0
  [09606e27] ODEInterfaceDiffEq v3.13.3
  [6fe1bfb0] OffsetArrays v1.14.1
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.87.0
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [65888b18] ParameterizedFunctions v5.17.0
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.2.0
  [995b91a9] PlotUtils v1.4.1
  [91a5bcdd] Plots v1.40.5
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.15
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.22
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [43287f4e] PtrArrays v1.2.0
⌃ [1fd47b50] QuadGK v2.10.0
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.5.3
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v3.26.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.7.1
  [47965b36] RootedTrees v2.23.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.46.0
  [31c91b34] SciMLBenchmarks v0.1.3
  [c0aeaf25] SciMLOperators v0.3.8
  [53ae85a6] SciMLStructures v1.4.1
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.1.0
  [727e6d20] SimpleNonlinearSolve v1.11.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [b85f4697] SoftGlobalScope v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.19.0
  [0a514795] SparseMatrixColorings v0.3.5
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.5.1
  [90137ffa] StaticArrays v1.9.7
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.1
  [7792a7ef] StrideArraysCore v0.5.7
  [69024149] StringEncodings v0.3.7
  [09ab397b] StructArrays v0.6.18
  [c3572dad] Sundials v4.24.0
  [2efcf032] SymbolicIndexingInterface v0.3.26
  [19f23fe9] SymbolicLimits v0.2.1
  [d1185830] SymbolicUtils v2.1.2
  [0c5d862f] Symbolics v5.34.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.4.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [0796e94c] Tokenize v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.1
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.70
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [44d3d7a6] Weave v0.10.12
  [ddb6d928] YAML v0.4.12
  [c2297ded] ZMQ v1.2.6
  [6e34b625] Bzip2_jll v1.0.8+1
  [83423d85] Cairo_jll v1.18.0+2
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+0
  [d2c73de3] GR_jll v0.73.7+0
  [78b55507] Gettext_jll v0.21.0+0
  [f8c6e375] Git_jll v2.44.0+2
  [7746bdde] Glib_jll v2.80.2+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [1d5cc7b8] IntelOpenMP_jll v2024.2.0+0
  [aacddb02] JpegTurbo_jll v3.0.3+0
  [c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
  [1d63c593] LLVMOpenMP_jll v15.0.7+0
  [aae0fff6] LSODA_jll v0.1.2+0
  [dd4b983a] LZO_jll v2.10.2+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.11+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.49.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.40.1+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [c771fb93] ODEInterface_jll v0.0.1+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.14+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [629bc702] Qt6Declarative_jll v6.7.1+2
  [ce943373] Qt6ShaderTools_jll v6.7.1+1
  [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.4.2+0
⌅ [fb77eaff] Sundials_jll v5.2.2+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.1+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.4.6+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [8f1865be] ZeroMQ_jll v4.3.5+0
  [3161d3a3] Zstd_jll v1.5.6+0
  [35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.43+1
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [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`