Transistor Amplifier, DAE format
using DiffEqDevTools, Sundials, ODEInterfaceDiffEq,
Plots, DASSL, DASKR
using ModelingToolkit, OrdinaryDiffEq
using ModelingToolkit: t_nounits as t, D_nounits as D
using LinearAlgebra
@parameters begin
Ub=6.0
UF=0.026
α=0.99
β=1e-6
R₀=1e3
R₁=9e3
R₂=9e3
R₃=9e3
R₄=9e3
R₅=9e3
R₆=9e3
R₇=9e3
R₈=9e3
R₉=9e3
C₁=1e-6
C₂=2e-6
C₃=3e-6
C₄=4e-6
C₅=5e-6
end
@variables begin
y₁(t) = 0.0
y₂(t) = 3.0 # Ub/(R₂/R₁ + 1)
y₃(t) = 3.0
y₄(t) = 6.0
y₅(t) = 3.0 # Ub/(R₆/R₅ + 1)
y₆(t) = 3.0
y₇(t) = 6.0
y₈(t) = 0.0
tmp1(t)
tmp2(t)
tmp3(t)
tmp4(t)
tmp5(t)
tmp6(t)
end
Uₑ = 0.1sin(200π * t)
g(x) = β * (exp(x / UF) - 1)
eqs = [
tmp1 ~ (-Uₑ / R₀ + y₁ / R₀) / C₁
tmp2 ~ (-Ub / R₂ + y₂ * (1 / R₁ + 1 / R₂) - (α - 1) * g(y₂ - y₃))/C₁
D(y₂) - D(y₁) ~ tmp1
D(y₁) - D(y₂) ~ tmp2
-C₂ * D(y₃) ~ -g(y₂ - y₃) + y₃/R₃
tmp5 ~ (-Ub / R₄ + y₄ / R₄ + α * g(y₂ - y₃))/C₃
tmp6 ~ (-Ub / R₆ + y₅ * (1 / R₅ + 1 / R₆) - (α - 1) * g(y₅ - y₆))/C₃
D(y₅) - D(y₄) ~ tmp5
-D(y₅) + D(y₄) ~ tmp6
-C₄ * D(y₆) ~ -g(y₅ - y₆) + y₆ / R₇
tmp3 ~ (-Ub / R₈ + y₇ / R₈ + α * g(y₅ - y₆) )/C₅
tmp4 ~ (y₈ / R₉) / C₅
-D(y₇) + D(y₈) ~ tmp3
D(y₇) - D(y₈) ~ tmp4
]
u0 = [y₁ => 0.0
y₂ => 3.0
y₃ => 3.0
y₄ => 6.0
y₅ => 3.0
y₆ => 3.0
y₇ => 6.0
y₈ => 0.0
]
@mtkbuild sys = ODESystem(eqs, t)
tspan = (0.0, 0.2)
mtkprob = ODEProblem(sys, u0, tspan)
ref_sol = solve(mtkprob, Rodas5P(), abstol = 1e-10, reltol = 1e-10)
du = mtkprob.f(mtkprob.u0, mtkprob.p, 0.0)
du0 = D.(unknowns(sys)) .=> du
daeprob = DAEProblem(sys, du0, [], tspan)
dae_ref_sol = solve(daeprob, IDA(), abstol = 1/10^7, reltol = 1/10^7)
function transamp(du, u, p, t)
y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈ = u
Uₑ = 0.1sin(200π * t)
Ub=6.0
UF=0.026
α=0.99
β=1e-6
R₀=1e3
R₁=9e3
R₂=9e3
R₃=9e3
R₄=9e3
R₅=9e3
R₆=9e3
R₇=9e3
R₈=9e3
R₉=9e3
C₁=1e-6
C₂=2e-6
C₃=3e-6
C₄=4e-6
C₅=5e-6
g(x) = β * (exp(x / UF) - 1)
du[1] = -Uₑ / R₀ + y₁ / R₀
du[2] = -Ub / R₂ + y₂ * (1 / R₁ + 1 / R₂) - (α - 1) * g(y₂ - y₃)
du[3] = -g(y₂ - y₃) + y₃/R₃
du[4] = -Ub / R₄ + y₄ / R₄ + α * g(y₂ - y₃)
du[5] = -Ub / R₆ + y₅ * (1 / R₅ + 1 / R₆) - (α - 1) * g(y₅ - y₆)
du[6] = -g(y₅ - y₆) + y₆ / R₇
du[7] = -Ub / R₈ + y₇ / R₈ + α * g(y₅ - y₆)
du[8] = y₈ / R₉
nothing
end
dirMassMatrix =
Float64.(ModelingToolkit.unwrap.(substitute.(
[-C₁ C₁ 0 0 0 0 0 0
C₁ -C₁ 0 0 0 0 0 0
0 0 -C₂ 0 0 0 0 0
0 0 0 -C₃ C₃ 0 0 0
0 0 0 C₃ -C₃ 0 0 0
0 0 0 0 0 -C₄ 0 0
0 0 0 0 0 0 -C₅ C₅
0 0 0 0 0 0 C₅ -C₅],
(parameters(sys) .=> ModelingToolkit.getdefault.(parameters(sys)),))))
mmf = ODEFunction(transamp, mass_matrix = dirMassMatrix)
mmprob = ODEProblem(mmf, [0.0,3.0,3.0,6.0,3.0,3.0,6.0,0.0], tspan)
mm_refsol = solve(mmprob, Rodas5(), reltol = 1e-12, abstol = 1e-12)
probs = [mtkprob,daeprob,mmprob]
refs = [ref_sol,ref_sol,mm_refsol];plot(ref_sol, idxs = [y₁,y₂,y₃,y₄,y₅,y₆,y₇,y₈])
plot(mm_refsol)
Omissions
DASSL.dassl()) is omitted because it throws a singularity error. rodas() is too slow at low tolerances.
High Tolerances
abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (1:4);
setups = [Dict(:prob_choice => 1, :alg=>Rodas4()),
Dict(:prob_choice => 1, :alg=>FBDF()),
Dict(:prob_choice => 1, :alg=>QNDF()),
Dict(:prob_choice => 1, :alg=>radau()),
Dict(:prob_choice => 1, :alg=>RadauIIA5()),
Dict(:prob_choice => 2, :alg=>DFBDF()),
Dict(:prob_choice => 2, :alg=>IDA()),
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;
save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10)
plot(wp)EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 9.8813129168249309E-324
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.9762625833649862E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
abstols = 1.0 ./ 10.0 .^ (6:8)
reltols = 1.0 ./ 10.0 .^ (2:4);
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()),
Dict(:prob_choice => 1, :alg=>Rodas4()),
Dict(:prob_choice => 2, :alg=>IDA()),
Dict(:prob_choice => 3, :alg=>Rodas5P()),
Dict(:prob_choice => 3, :alg=>Rodas4()),
Dict(:prob_choice => 3, :alg=>rodas()),
Dict(:prob_choice => 3, :alg=>FBDF()),
Dict(:prob_choice => 2, :alg=>IDA()),
Dict(:prob_choice => 2, :alg=>DASKR.daskr()),
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;
save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10)
plot(wp)DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1049635569445D-15
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1679416911111D-15
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.6717667644445D-16
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
Timeseries Errors
abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (1:4);
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()),
Dict(:prob_choice => 1, :alg=>Rodas4()),
Dict(:prob_choice => 1, :alg=>FBDF()),
Dict(:prob_choice => 1, :alg=>QNDF()),
Dict(:prob_choice => 1, :alg=>radau()),
Dict(:prob_choice => 1, :alg=>RadauIIA5()),
Dict(:prob_choice => 2, :alg=>DFBDF()),
Dict(:prob_choice => 2, :alg=>IDA()),
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;error_estimate = :l2,
save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10)
plot(wp)EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 9.8813129168249309E-324
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.9762625833649862E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
abstols = 1.0 ./ 10.0 .^ (6:8)
reltols = 1.0 ./ 10.0 .^ (2:4);
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()),
Dict(:prob_choice => 1, :alg=>Rodas4()),
Dict(:prob_choice => 2, :alg=>IDA()),
Dict(:prob_choice => 3, :alg=>Rodas5P()),
Dict(:prob_choice => 3, :alg=>Rodas4()),
Dict(:prob_choice => 3, :alg=>rodas()),
Dict(:prob_choice => 3, :alg=>FBDF()),
Dict(:prob_choice => 2, :alg=>IDA()),
Dict(:prob_choice => 2, :alg=>DASKR.daskr()),
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;error_estimate = :l2,
save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10)
plot(wp)DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1049635569445D-15
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1679416911111D-15
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.6717667644445D-16
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
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(:prob_choice => 1, :alg=>Rodas5P()),
Dict(:prob_choice => 3, :alg=>Rodas5P()),
Dict(:prob_choice => 1, :alg=>Rodas4()),
Dict(:prob_choice => 3, :alg=>Rodas4()),
Dict(:prob_choice => 1, :alg=>FBDF()),
Dict(:prob_choice => 1, :alg=>QNDF()),
Dict(:prob_choice => 1, :alg=>radau()),
Dict(:prob_choice => 1, :alg=>RadauIIA5()),
Dict(:prob_choice => 2, :alg=>DFBDF()),
Dict(:prob_choice => 2, :alg=>IDA()),
Dict(:prob_choice => 2, :alg=>DASKR.daskr()),
]
wp = WorkPrecisionSet(probs,abstols,reltols,setups;
save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10)
plot(wp)EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 9.8813129168249309E-324
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1679416822793D-15
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.6717667291172D-16
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1074826766588D-15
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1719722826540D-15
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.6878891306160D-16
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.2751556522464D-16
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
wp = WorkPrecisionSet(probs,abstols,reltols,setups;error_estimate = :l2,
save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10)
plot(wp)EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 9.8813129168249309E-324
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
EXIT OF RADAU AT X= 0.0000E+00
STEP SIZE T0O SMALL, H= 1.4821969375237396E-323
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1679416822793D-15
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.6717667291172D-16
DASKR-- ERROR TEST FAILED REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1074826766588D-15
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.1719722826540D-15
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.6878891306160D-16
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
DASKR-- AT T (=R1) AND STEPSIZE H (=R2) THE
In above, R1 = 0.0000000000000D+00 R2 = 0.2751556522464D-16
DASKR-- NONLINEAR SOLVER FAILED TO CONVERGE
DASKR-- REPEATEDLY OR WITH ABS(H)=HMIN
Conclusion
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/DAE","TransistorAmplifier.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: 128 default, 0 interactive, 64 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/DAE/Project.toml`
[165a45c3] DASKR v2.9.1
[e993076c] DASSL v2.6.1
[f3b72e0c] DiffEqDevTools v2.44.4
[961ee093] ModelingToolkit v9.24.0
[09606e27] ODEInterfaceDiffEq v3.13.3
[1dea7af3] OrdinaryDiffEq v6.85.0
[91a5bcdd] Plots v1.40.5
[31c91b34] SciMLBenchmarks v0.1.3
[c3572dad] Sundials v4.24.0And the full manifest:
Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/DAE/Manifest.toml`
[47edcb42] ADTypes v1.6.0
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.36
[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
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[3da002f7] ColorTypes v0.11.5
[c3611d14] ColorVectorSpace v0.10.0
[5ae59095] Colors v0.12.11
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[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
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[a8cc5b0e] Crayons v4.1.1
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[e993076c] DASSL v2.6.1
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[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 v9.24.0
[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 v6.85.0
[90014a1f] PDMats v0.11.31
[65ce6f38] PackageExtensionCompat v1.0.2
[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 v2.9.4
[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 v2.42.0
[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 v1.10.1
[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 v0.3.4
[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 v5.33.0
[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 v0.11.0
[d5829a12] TriangularSolve v0.2.1
[410a4b4d] Tricks v0.1.8
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.20.0
[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 v0.4.11
[c2297ded] ZMQ v1.2.6
[6e34b625] Bzip2_jll v1.0.8+1
[83423d85] Cairo_jll v1.18.0+2
[655fdf9c] DASKR_jll v1.0.0+0
[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 v0.73.6+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
[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
[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+1
[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`