GitHub

DifferentialEquations.jl: Efficient Differential Equation Solving in Julia

This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. Equations within the realm of this package include:

  • Discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations)
  • Ordinary differential equations (ODEs)
  • Split and Partitioned ODEs (Symplectic integrators, IMEX Methods)
  • Stochastic ordinary differential equations (SODEs or SDEs)
  • Stochastic differential-algebraic equations (SDAEs)
  • Random differential equations (RODEs or RDEs)
  • Differential algebraic equations (DAEs)
  • Delay differential equations (DDEs)
  • Neutral, retarded, and algebraic delay differential equations (NDDEs, RDDEs, and DDAEs)
  • Stochastic delay differential equations (SDDEs)
  • Experimental support for stochastic neutral, retarded, and algebraic delay differential equations (SNDDEs, SRDDEs, and SDDAEs)
  • Mixed discrete and continuous equations (Hybrid Equations, Jump Diffusions)
  • (Stochastic) partial differential equations ((S)PDEs) (with both finite difference and finite element methods)

The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research which routinely outperform the “standard” C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. At the same time, it wraps the classic C/Fortran methods, making it easy to switch over to them whenever necessary. Solving differential equations with different methods from different languages and packages can be done by changing one line of code, allowing for easy benchmarking to ensure you are using the fastest method possible.

DifferentialEquations.jl integrates with the Julia package sphere with:

  • GPU acceleration through CUDA.jl and DiffEqGPU.jl
  • Automated sparsity detection with Symbolics.jl
  • Automatic Jacobian coloring with SparseDiffTools.jl, allowing for fast solutions to problems with sparse or structured (Tridiagonal, Banded, BlockBanded, etc.) Jacobians
  • Allowing the specification of linear solvers for maximal efficiency with LinearSolve.jl
  • Progress meter integration with the Visual Studio Code IDE for estimated time to solution
  • Automatic plotting of time series and phase plots
  • Built-in interpolations
  • Wraps for common C/Fortran methods like Sundials and Hairer's radau
  • Arbitrary precision with BigFloats and Arbfloats
  • Arbitrary array types, allowing the definition of differential equations on matrices and distributed arrays
  • Unit checked arithmetic with Unitful

Additionally, DifferentialEquations.jl comes with built-in analysis features, including:

Contributing

Supporting and Citing

The software in this ecosystem was developed as part of academic research. If you would like to help support it, please star the repository, as such metrics may help us secure funding in the future. If you use SciML software as part of your research, teaching, or other activities, we would be grateful if you could cite our work as necessary for any use of DifferentialEquations.jl or the packages that are maintained as part of its suite (OrdinaryDiffEq.jl, Sundials.jl, DiffEqDevTools.jl, etc.).

@article{rackauckas2017differentialequations,
  title={Differential{E}quations.jl--a performant and feature-rich ecosystem for solving differential equations in {J}ulia},
  author={Rackauckas, Christopher and Nie, Qing},
  journal={Journal of Open Research Software},
  volume={5},
  number={1},
  year={2017},
  publisher={Ubiquity Press}
}

Additionally, many of the solvers utilize novel algorithms, and if these algorithms are used, we ask that you cite the methods. Please see our citation page for guidelines.

Getting Started: Installation And First Steps

Installing from Julia

To install the package, use the following command inside the Julia REPL:

using Pkg
Pkg.add("DifferentialEquations")

To load the package, use the command:

using DifferentialEquations

This will add solvers and dependencies for all kinds of Differential Equations (e.g. ODEs or SDEs etc., see the Supported Equations section below). If you are interested in only one type of equation solver of DifferentialEquations.jl or simply want a more lightweight version, see the Reduced Compile Time and Low Dependency Usage page.

To understand the package in more detail, check out the following tutorials in this manual. It is highly recommended that new users start with the ODE tutorial. Example IJulia notebooks can also be found in SciMLTutorials.jl. If you find any example where there appears to be an error, please open an issue.

For the most up-to-date information on using the package, please join the Julia Zulip channel.

Using the bleeding edge for the latest features and development is only recommended for power users. Information on how to get to the bleeding edge is found in the developer documentation.

Installing from Python

Use of DifferentialEquations.jl from the Python programming language is available through the diffeqpy module. To install diffeqpy, use pip:

pip install diffeqpy

Using diffeqpy requires that Julia is installed and in the path, along with DifferentialEquations.jl and PyCall.jl. To install Julia, download a generic binary from the JuliaLang site and add it to your path. To install Julia packages required for diffeqpy, open up Python interpreter then run:

>>> import diffeqpy
>>> diffeqpy.install()

and you're good! In addition, to improve the performance of your code, it is recommended that you use Numba to JIT compile your derivative functions. To install Numba, use:

pip install numba

diffeqpy supports the majority of DifferentialEquations.jl with very similar syntax, see the diffeqpy README for more details. One important point to note is that Numba is generally an order of magnitude slower than Julia in terms of the generated differential equation solver code, and thus it is recommended to use julia.Main.eval for Julia-side derivative function implementations for maximal efficiency. See this blog post for more information.

Installing from R

Use of DifferentialEquations.jl from the R programming language is available through the diffeqr module. diffeqr is registered into CRAN. Thus to add the package, use:

install.packages("diffeqr")

To install the master branch of the package (for developers), use:

devtools::install_github('SciML/diffeqr', build_vignettes=T)

You will need a working installation of Julia in your path. To install Julia, download a generic binary from the JuliaLang site and add it to your path. The download and installation of DifferentialEquations.jl will happen on the first invocation of diffeqr::diffeq_setup().

Currently, use from R supported a subset of DifferentialEquations.jl which is documented through CRAN.

Video Tutorial

Video Tutorial

Tutorials

The following tutorials will introduce you to the functionality of DifferentialEquations.jl. More examples can be found by checking out the IJulia notebooks in the examples folder.

Removing and Reducing Compile Times

In some situations, one may wish to decrease the compile time associated with DifferentialEquations.jl usage. If that's the case, there are two strategies to employ. One strategy is to use the low dependency usage. DifferentialEquations.jl is a metapackage composed of many smaller packages, and thus one could directly use a single component, such as OrdinaryDiffEq.jl for the pure Julia ODE solvers, and decrease the compile times by ignoring the rest (note: the interface is exactly the same, except using a solver apart from those in OrdinaryDiffEq.jl will error). We recommend that downstream packages rely solely on the packages they need.

The other strategy is to use PackageCompiler.jl to create a system image that precompiles the whole package. To do this, one simply does:

using PackageCompiler
PackageCompiler.create_sysimage([:DifferentialEquations, :Plots]; replace_default = true)

Note that there are some drawbacks to adding a package in your system image. For example, the package will never update until you manually rebuild the system image again. For more information on the consequences, see this portion of the PackageCompiler manual.

Basics

These pages introduce you to the core of DifferentialEquations.jl and the common interface. It explains the general workflow, options which are generally available, and the general tools for analysis.

Problem Types

These pages describe building the problem types to define differential equations for the solvers, and the special features of the different solution types.

Solver Algorithms

These pages describe the solvers and available algorithms in detail.

Additional Features

These sections discuss extra performance enhancements, event handling, and other in-depth features.

Extra Details

These are just assorted extra explanations for the curious.

Acknowledgements

Core Contributors

JuliaDiffEq and DifferentialEquations.jl has been a collaborative effort by many individuals. Significant contributions have been made by the following individuals:

  • Chris Rackauckas (@ChrisRackauckas) (lead developer)
  • Yingbo Ma (@YingboMa)
  • David Widmann (@devmotion)
  • Hendrik Ranocha (@ranocha)
  • Ethan Levien (@elevien)
  • Tom Short (@tshort)
  • @dextorious
  • Samuel Isaacson (@isaacsas)

Google Summer of Code Alumni

  • Yingbo Ma (@YingboMa)
  • Shivin Srivastava (@shivin9)
  • Ayush Pandey (@Ayush-iitkgp)
  • Xingjian Guo (@MSeeker1340)
  • Shubham Maddhashiya (@sipah00)
  • Vaibhav Kumar Dixit (@Vaibhavdixit02)

Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status `/var/lib/buildkite-agent/builds/gpuci-17/julialang/diffeqdocs-dot-jl/docs/Project.toml`
  [2169fc97] AlgebraicMultigrid v0.6.0
  [fbb218c0] BSON v0.3.7
  [ded0fc24] BVProblemLibrary v0.1.2
  [6e4b80f9] BenchmarkTools v1.3.2
  [764a87c0] BoundaryValueDiffEq v5.1.0
  [336ed68f] CSV v0.10.11
  [dfb8ca35] DAEProblemLibrary v0.1.0
  [165a45c3] DASKR v2.9.1
  [f42792ee] DDEProblemLibrary v0.1.2
  [a93c6f00] DataFrames v1.6.1
  [2b5f629d] DiffEqBase v6.132.0
  [459566f4] DiffEqCallbacks v2.33.0
  [d91efeb5] DiffEqDocs v7.8.0 `/var/lib/buildkite-agent/builds/gpuci-17/julialang/diffeqdocs-dot-jl`
  [0c46a032] DifferentialEquations v7.11.0
  [31c24e10] Distributions v0.25.102
  [e30172f5] Documenter v1.1.0
  [6a86dc24] FiniteDiff v2.21.1
  [f6369f11] ForwardDiff v0.10.36
  [40713840] IncompleteLU v0.2.1
  [033835bb] JLD2 v0.4.35
  [faf0f6d7] JumpProblemLibrary v0.1.4
  [961ee093] ModelingToolkit v8.71.2
  [fdc4e326] ODEProblemLibrary v0.1.7
  [7f7a1694] Optimization v3.19.1
  [4e6fcdb7] OptimizationNLopt v0.1.8
  [1dea7af3] OrdinaryDiffEq v6.58.0
  [91a5bcdd] Plots v1.39.0
  [731186ca] RecursiveArrayTools v2.38.10
  [c72e72a9] SDEProblemLibrary v0.1.6
  [0bca4576] SciMLBase v2.3.0
  [c0aeaf25] SciMLOperators v0.3.6
  [90137ffa] StaticArrays v1.6.5
  [c3572dad] Sundials v4.20.0
  [0c5d862f] Symbolics v5.8.0
  [1986cc42] Unitful v1.17.0
and using this machine and Julia version.
Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 48 × AMD EPYC 7402 24-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, znver2)
  Threads: 1 on 2 virtual cores
Environment:
  JULIA_CPU_THREADS = 2
  JULIA_DEBUG = Documenter
  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/0185fce3-4489-413a-a934-123dd653ef61
  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
  JULIA_PKG_SERVER =
A more complete overview of all dependencies and their versions is also provided.
Status `/var/lib/buildkite-agent/builds/gpuci-17/julialang/diffeqdocs-dot-jl/docs/Manifest.toml`
  [47edcb42] ADTypes v0.2.4
  [a4c015fc] ANSIColoredPrinters v0.0.1
  [c3fe647b] AbstractAlgebra v0.32.5
  [1520ce14] AbstractTrees v0.4.4
  [79e6a3ab] Adapt v3.6.2
  [2169fc97] AlgebraicMultigrid v0.6.0
  [ec485272] ArnoldiMethod v0.2.0
  [4fba245c] ArrayInterface v7.4.11
  [30b0a656] ArrayInterfaceCore v0.1.29
  [fbb218c0] BSON v0.3.7
  [ded0fc24] BVProblemLibrary v0.1.2
  [6e4b80f9] BenchmarkTools v1.3.2
  [e2ed5e7c] Bijections v0.1.5
  [d1d4a3ce] BitFlags v0.1.7
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
  [764a87c0] BoundaryValueDiffEq v5.1.0
⌅ [fa961155] CEnum v0.4.2
  [2a0fbf3d] CPUSummary v0.2.4
  [00ebfdb7] CSTParser v3.3.6
  [336ed68f] CSV v0.10.11
  [49dc2e85] Calculus v0.5.1
  [479239e8] Catalyst v13.5.0
  [d360d2e6] ChainRulesCore v1.16.0
  [fb6a15b2] CloseOpenIntervals v0.1.12
  [523fee87] CodecBzip2 v0.8.0
  [944b1d66] CodecZlib v0.7.2
  [35d6a980] ColorSchemes v3.24.0
  [3da002f7] ColorTypes v0.11.4
  [c3611d14] ColorVectorSpace v0.10.0
  [5ae59095] Colors v0.12.10
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.10.0
  [b152e2b5] CompositeTypes v0.1.3
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.2.1
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.5.4
  [d38c429a] Contour v0.6.2
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [dfb8ca35] DAEProblemLibrary v0.1.0
  [165a45c3] DASKR v2.9.1
  [f42792ee] DDEProblemLibrary v0.1.2
  [9a962f9c] DataAPI v1.15.0
  [a93c6f00] DataFrames v1.6.1
  [864edb3b] DataStructures v0.18.15
  [e2d170a0] DataValueInterfaces v1.0.0
  [bcd4f6db] DelayDiffEq v5.43.1
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.132.0
  [459566f4] DiffEqCallbacks v2.33.0
  [d91efeb5] DiffEqDocs v7.8.0 `/var/lib/buildkite-agent/builds/gpuci-17/julialang/diffeqdocs-dot-jl`
  [77a26b50] DiffEqNoiseProcess v5.19.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.11.0
  [b4f34e82] Distances v0.10.10
  [31c24e10] Distributions v0.25.102
  [ffbed154] DocStringExtensions v0.9.3
  [e30172f5] Documenter v1.1.0
  [5b8099bc] DomainSets v0.6.7
  [fa6b7ba4] DualNumbers v0.6.8
  [7c1d4256] DynamicPolynomials v0.5.3
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.6.0
  [460bff9d] ExceptionUnwrapping v0.1.9
  [d4d017d3] ExponentialUtilities v1.25.0
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.1
  [7034ab61] FastBroadcast v0.2.6
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.0
  [5789e2e9] FileIO v1.16.1
  [48062228] FilePathsBase v0.9.21
  [1a297f60] FillArrays v1.6.1
  [6a86dc24] FiniteDiff v2.21.1
  [53c48c17] FixedPointNumbers v0.8.4
  [59287772] Formatting v0.4.2
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.5
  [46192b85] GPUArraysCore v0.1.5
  [28b8d3ca] GR v0.72.10
  [c145ed77] GenericSchur v0.5.3
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.9.0
  [42e2da0e] Grisu v1.0.2
  [0b43b601] Groebner v0.4.4
  [d5909c97] GroupsCore v0.4.0
  [cd3eb016] HTTP v1.10.0
  [3e5b6fbb] HostCPUFeatures v0.1.16
  [34004b35] HypergeometricFunctions v0.3.23
  [b5f81e59] IOCapture v0.2.3
  [615f187c] IfElse v0.1.1
  [40713840] IncompleteLU v0.2.1
  [d25df0c9] Inflate v0.1.3
  [842dd82b] InlineStrings v1.4.0
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.7
  [41ab1584] InvertedIndices v1.3.0
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [033835bb] JLD2 v0.4.35
  [1019f520] JLFzf v0.1.5
  [692b3bcd] JLLWrappers v1.5.0
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.39
  [faf0f6d7] JumpProblemLibrary v0.1.4
  [ccbc3e58] JumpProcesses v9.8.0
  [ef3ab10e] KLU v0.4.1
  [ba0b0d4f] Krylov v0.9.4
  [b964fa9f] LaTeXStrings v1.3.0
  [2ee39098] LabelledArrays v1.14.0
  [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.1
  [10f19ff3] LayoutPointers v0.1.14
  [0e77f7df] LazilyInitializedFields v1.2.1
  [50d2b5c4] Lazy v0.15.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.9.2
  [2ab3a3ac] LogExpFunctions v0.3.26
  [e6f89c97] LoggingExtras v1.0.3
  [bdcacae8] LoopVectorization v0.12.165
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.11
  [d125e4d3] ManualMemory v0.1.8
  [d0879d2d] MarkdownAST v0.1.2
  [b8f27783] MathOptInterface v1.20.1
  [fdba3010] MathProgBase v0.7.8
  [739be429] MbedTLS v1.1.7
  [442fdcdd] Measures v0.3.2
  [e1d29d7a] Missings v1.1.0
  [961ee093] ModelingToolkit v8.71.2
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.2
  [d8a4904e] MutableArithmetics v1.3.3
  [d41bc354] NLSolversBase v7.8.3
⌅ [76087f3c] NLopt v0.6.5
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v2.1.0
  [fdc4e326] ODEProblemLibrary v0.1.7
  [6fe1bfb0] OffsetArrays v1.12.10
  [4d8831e6] OpenSSL v1.4.1
  [429524aa] Optim v1.7.7
  [7f7a1694] Optimization v3.19.1
  [4e6fcdb7] OptimizationNLopt v0.1.8
  [bac558e1] OrderedCollections v1.6.2
  [1dea7af3] OrdinaryDiffEq v6.58.0
  [90014a1f] PDMats v0.11.25
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.7.2
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.1.0
  [995b91a9] PlotUtils v1.3.5
  [91a5bcdd] Plots v1.39.0
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.7
  [1d0040c9] PolyesterWeave v0.2.1
  [2dfb63ee] PooledArrays v1.4.3
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.12
  [aea7be01] PrecompileTools v1.2.0
  [21216c6a] Preferences v1.4.1
  [08abe8d2] PrettyTables v2.2.7
  [27ebfcd6] Primes v0.5.4
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.9.0
  [1fd47b50] QuadGK v2.9.1
  [74087812] Random123 v1.6.1
  [fb686558] RandomExtensions v0.4.3
  [e6cf234a] RandomNumbers v1.5.3
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v2.38.10
  [f2c3362d] RecursiveFactorization v0.2.20
  [189a3867] Reexport v1.2.2
  [2792f1a3] RegistryInstances v0.1.0
  [05181044] RelocatableFolders v1.0.0
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
  [c72e72a9] SDEProblemLibrary v0.1.6
  [fdea26ae] SIMD v3.4.5
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.39
  [0bca4576] SciMLBase v2.3.0
  [e9a6253c] SciMLNLSolve v0.1.9
  [c0aeaf25] SciMLOperators v0.3.6
  [6c6a2e73] Scratch v1.2.0
  [91c51154] SentinelArrays v1.4.0
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.1.0
  [727e6d20] SimpleNonlinearSolve v0.1.20
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [66db9d55] SnoopPrecompile v1.0.3
  [a2af1166] SortingAlgorithms v1.1.1
  [47a9eef4] SparseDiffTools v2.7.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.3.1
  [aedffcd0] Static v0.8.8
  [0d7ed370] StaticArrayInterface v1.4.1
  [90137ffa] StaticArrays v1.6.5
  [1e83bf80] StaticArraysCore v1.4.2
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.2
  [4c63d2b9] StatsFuns v1.3.0
  [9672c7b4] SteadyStateDiffEq v1.16.1
  [789caeaf] StochasticDiffEq v6.63.0
  [7792a7ef] StrideArraysCore v0.4.17
  [892a3eda] StringManipulation v0.3.4
  [c3572dad] Sundials v4.20.0
  [2efcf032] SymbolicIndexingInterface v0.2.2
  [d1185830] SymbolicUtils v1.4.0
  [0c5d862f] Symbolics v5.8.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.0
  [62fd8b95] TensorCore v0.1.1
  [5d786b92] TerminalLoggers v0.1.7
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.23
  [0796e94c] Tokenize v0.5.25
  [3bb67fe8] TranscodingStreams v0.9.13
  [a2a6695c] TreeViews v0.3.0
  [d5829a12] TriangularSolve v0.1.19
  [410a4b4d] Tricks v0.1.7
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.17.0
  [45397f5d] UnitfulLatexify v1.6.3
  [a7c27f48] Unityper v0.1.5
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.64
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [76eceee3] WorkerUtilities v1.6.1
  [700de1a5] ZygoteRules v0.2.3
  [6e34b625] Bzip2_jll v1.0.8+0
  [83423d85] Cairo_jll v1.16.1+1
  [655fdf9c] DASKR_jll v1.0.0+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.5.0+0
⌃ [b22a6f82] FFMPEG_jll v4.4.2+2
  [a3f928ae] Fontconfig_jll v2.13.93+0
  [d7e528f0] FreeType2_jll v2.13.1+0
  [559328eb] FriBidi_jll v1.0.10+0
  [0656b61e] GLFW_jll v3.3.8+0
  [d2c73de3] GR_jll v0.72.10+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.76.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [1d5cc7b8] IntelOpenMP_jll v2023.2.0+0
  [aacddb02] JpegTurbo_jll v2.1.91+0
  [c1c5ebd0] LAME_jll v3.100.1+0
  [88015f11] LERC_jll v3.0.0+1
  [1d63c593] LLVMOpenMP_jll v15.0.4+0
  [dd4b983a] LZO_jll v2.10.1+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.7+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.42.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.35.0+0
  [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.36.0+0
  [856f044c] MKL_jll v2023.2.0+0
  [079eb43e] NLopt_jll v2.7.1+0
  [e7412a2a] Ogg_jll v1.3.5+1
⌅ [458c3c95] OpenSSL_jll v1.1.23+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [30392449] Pixman_jll v0.42.2+0
  [c0090381] Qt6Base_jll v6.5.2+2
  [f50d1b31] Rmath_jll v0.4.0+0
⌅ [fb77eaff] Sundials_jll v5.2.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.25.0+0
  [02c8fc9c] XML2_jll v2.11.5+0
  [aed1982a] XSLT_jll v1.1.34+0
  [ffd25f8a] XZ_jll v5.4.4+0
  [f67eecfb] Xorg_libICE_jll v1.0.10+1
  [c834827a] Xorg_libSM_jll v1.2.3+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 v1.3.4+4
  [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 v0.9.10+4
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.15.0+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
  [3161d3a3] Zstd_jll v1.5.5+0
  [35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.29.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.4.0+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 v1.6.38+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+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 v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.9.2
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics v1.9.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.0.5+0
  [deac9b47] LibCURL_jll v7.84.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [c8ffd9c3] MbedTLS_jll v2.28.2+0
  [14a3606d] MozillaCACerts_jll v2022.10.11
  [4536629a] OpenBLAS_jll v0.3.21+4
  [05823500] OpenLibm_jll v0.8.1+0
  [efcefdf7] PCRE2_jll v10.42.0+0
  [bea87d4a] SuiteSparse_jll v5.10.1+6
  [83775a58] Zlib_jll v1.2.13+0
  [8e850b90] libblastrampoline_jll v5.8.0+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+0
Info Packages marked with ⌃ and ⌅ have new versions available, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.