Lotka_Volterra tutorial

Specific Domains
1

Hi, I tried the first tutorial: "Optimizing parameters of an ODE for an Optimal Control Problem. I executed all the functions up to and including "p = [1.5, 1.0, 3.0, 1.0]. Then I typed:

 prob = ODEProblem(lotka_volterra, u0, tspan, p)

and got the following error message, which I cannot figure out.
I am using Julia 1.4 (perhaps that is the reason?)

julia> prob = ODEProblem(lotka_volterra, u0, tspan, p)
soERROR: l MethodError: no method matching promote_tspan(::Array{Float64,1})
Closest candidates are:
promote_tspan(::Nothing) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/problem_utils.jl:9
promote_tspan(::Tuple{T,S}) where {T, S} at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/problem_utils.jl:7
promote_tspan(::Number) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/problem_utils.jl:8
…
Stacktrace:=
[1] ODEProblem{true,tType,isinplace,P,F,K,PT} where PT where K where F where P where isinplace where tType(::ODEFunction{true,typeof(lotka_volterra),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::DiffEqBase.StandardODEProblem; kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/ode_problems.jl:34
[2] ODEProblem{true,tType,isinplace,P,F,K,PT} where PT where K where F where P where isinplace where tType(::ODEFunction{true,typeof(lotka_volterra),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::DiffEqBase.StandardODEProblem) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/ode_problems.jl:34 (repeats 2 times)
[3] ODEProblem(::ODEFunction{true,typeof(lotka_volterra),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}; kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/ode_problems.jl:72
[4] ODEProblem(::ODEFunction{true,typeof(lotka_volterra),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/ode_problems.jl:72
[5] ODEProblem(::Function, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}; kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/ode_problems.jl:76
[6] ODEProblem(::Function, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/erlebach/.julia/packages/DiffEqBase/LNYfU/src/problems/ode_problems.jl:76
[7] top-level scope at none:0

2

Did you make tspan an array instead of a tuple? I.e., (0.0,10.0) vs [0.0,10.0]?

3

I do not know, Chris, and I returned to Julia 1.3 to try it out again. This time, I will pay more attention. If it works, I will return to Julia 1.4 .

Side question: the recompiling of libraries already drives me nuts. What must I do (with version 1.4 I assume) to have the libraries maintained in their compiled state? Or is this automatic and they are kept somewhere under ~/.julia?

I will reply to the very nice email you sent me at a later time. I wanted to develop some more knowledge before commenting again.

4

Using version 1.3 of Julia, I got further, so I must have typed […] instead of (…] for tspan. Thank you, Chris. Must be a common error.

However, I could not add the DiffEqFlux package in Julia 1.3 . Is that expected? Thanks.

(v1.3) pkg> add DiffEqFlux
Resolving package versions…
ERROR: Unsatisfiable requirements detected for package DiffEqSensitivity [41bf760c]:
DiffEqSensitivity [41bf760c] log:
├─possible versions are: [2.0.0, 2.1.0-2.1.1, 2.2.0, 2.3.0, 2.4.0, 3.0.0-3.0.2, 3.1.0, 3.2.0-3.2.4, 3.3.0-3.3.2, 4.0.0-4.0.1, 4.1.0-4.1.3, 4.2.0, 4.3.0, 4.4.0, 5.0.0, 5.1.0-5.1.3, 6.0.0-6.0.1, 6.1.0, 6.2.0, 6.3.0, 6.4.0, 6.5.0-6.5.3, 6.6.0-6.6.2] or uninstalled
├─restricted by compatibility requirements with DiffEqFlux [aae7a2af] to versions: [2.0.0, 2.1.0-2.1.1, 2.2.0, 2.3.0, 2.4.0, 3.0.0-3.0.2, 3.1.0, 3.2.0-3.2.4, 3.3.0-3.3.2, 4.0.0-4.0.1, 4.1.0-4.1.3, 4.2.0, 4.3.0, 4.4.0, 5.0.0, 5.1.0-5.1.3]
│ └─DiffEqFlux [aae7a2af] log:
│ ├─possible versions are: [0.0.1, 0.1.0, 0.2.0, 0.3.0, 0.4.0, 0.5.0-0.5.2, 0.6.0-0.6.1, 0.7.0, 0.8.0-0.8.1, 0.9.0, 0.10.0-0.10.2, 1.0.0, 1.1.0-1.1.1, 1.2.0-1.2.2, 1.3.0-1.3.2] or uninstalled
│ ├─restricted to versions * by an explicit requirement, leaving only versions [0.0.1, 0.1.0, 0.2.0, 0.3.0, 0.4.0, 0.5.0-0.5.2, 0.6.0-0.6.1, 0.7.0, 0.8.0-0.8.1, 0.9.0, 0.10.0-0.10.2, 1.0.0, 1.1.0-1.1.1, 1.2.0-1.2.2, 1.3.0-1.3.2]
│ ├─restricted by compatibility requirements with Juno [e5e0dc1b] to versions: [0.0.1, 0.1.0, 0.2.0, 0.3.0, 0.4.0, 0.5.0-0.5.2, 0.6.0-0.6.1, 0.7.0, 0.8.0-0.8.1, 0.9.0, 0.10.0-0.10.2, 1.0.0, 1.1.0-1.1.1, 1.3.2] or uninstalled, leaving only versions: [0.0.1, 0.1.0, 0.2.0, 0.3.0, 0.4.0, 0.5.0-0.5.2, 0.6.0-0.6.1, 0.7.0, 0.8.0-0.8.1, 0.9.0, 0.10.0-0.10.2, 1.0.0, 1.1.0-1.1.1, 1.3.2]
│ │ └─Juno [e5e0dc1b] log:
│ │ ├─possible versions are: [0.5.0-0.5.5, 0.6.0, 0.7.0-0.7.2, 0.8.0] or uninstalled
│ │ └─restricted to versions 0.8.0 by an explicit requirement, leaving only versions 0.8.0
│ ├─restricted by compatibility requirements with Flux [587475ba] to versions: [0.0.1, 0.1.0, 0.2.0, 0.3.0, 0.4.0, 0.5.0-0.5.2, 0.6.0-0.6.1, 0.7.0, 0.8.0-0.8.1, 0.9.0, 0.10.0-0.10.2] or uninstalled, leaving only versions: [0.0.1, 0.1.0, 0.2.0, 0.3.0, 0.4.0, 0.5.0-0.5.2, 0.6.0-0.6.1, 0.7.0, 0.8.0-0.8.1, 0.9.0, 0.10.0-0.10.2]
│ │ └─Flux [587475ba] log:
│ │ ├─possible versions are: [0.4.1, 0.5.0-0.5.4, 0.6.0-0.6.10, 0.7.0-0.7.3, 0.8.0-0.8.3, 0.9.0, 0.10.0-0.10.1] or uninstalled
│ │ └─restricted to versions 0.9.0 by an explicit requirement, leaving only versions 0.9.0
│ └─restricted by compatibility requirements with RecursiveArrayTools [731186ca] to versions: [0.0.1, 0.1.0, 0.2.0, 0.3.0, 1.0.0, 1.1.0-1.1.1, 1.2.0-1.2.2, 1.3.0-1.3.2] or uninstalled, leaving only versions: [0.0.1, 0.1.0, 0.2.0, 0.3.0]
│ └─RecursiveArrayTools [731186ca] log:
│ ├─possible versions are: [0.16.0-0.16.3, 0.17.0-0.17.2, 0.18.0-0.18.6, 0.19.0-0.19.1, 0.20.0, 1.0.0-1.0.2, 1.1.0-1.1.1, 1.2.0-1.2.1, 2.0.0-2.0.5, 2.1.0] or uninstalled
│ ├─restricted by compatibility requirements with DifferentialEquations [0c46a032] to versions: [2.0.0-2.0.5, 2.1.0]
│ │ └─DifferentialEquations [0c46a032] log:
│ │ ├─possible versions are: [5.0.0, 5.1.0, 5.2.0-5.2.1, 5.3.0-5.3.1, 6.0.0, 6.1.0, 6.2.0, 6.3.0, 6.4.0, 6.6.0, 6.7.0, 6.8.0, 6.9.0, 6.10.0-6.10.1, 6.11.0] or uninstalled
│ │ └─restricted to versions 6.11.0 by an explicit requirement, leaving only versions 6.11.0
│ └─restricted by compatibility requirements with RecipesBase [3cdcf5f2] to versions: 2.1.0 or uninstalled, leaving only versions: 2.1.0
│ └─RecipesBase [3cdcf5f2] log:
│ ├─possible versions are: [0.4.0, 0.5.0, 0.6.0, 0.7.0, 0.8.0] or uninstalled
│ └─restricted by compatibility requirements with Plots [91a5bcdd] to versions: 0.8.0
│ └─Plots [91a5bcdd] log:
│ ├─possible versions are: [0.12.1-0.12.4, 0.13.0-0.13.1, 0.14.0-0.14.2, 0.15.0-0.15.1, 0.16.0, 0.17.0-0.17.4, 0.18.0, 0.19.0-0.19.3, 0.20.0-0.20.6, 0.21.0, 0.22.0-0.22.5, 0.23.0-0.23.2, 0.24.0, 0.25.0-0.25.3, 0.26.0-0.26.3, 0.27.0-0.27.1, 0.28.0-0.28.4, 0.29.0-0.29.1] or uninstalled
│ └─restricted to versions 0.29.1 by an explicit requirement, leaving only versions 0.29.1
├─restricted by compatibility requirements with RecursiveArrayTools [731186ca] to versions: [4.3.0, 6.3.0, 6.4.0, 6.5.0-6.5.3, 6.6.0-6.6.2] or uninstalled, leaving only versions: 4.3.0
│ └─RecursiveArrayTools [731186ca] log: see above
└─restricted by compatibility requirements with DiffEqFlux [aae7a2af] to versions: [2.0.0, 2.1.0-2.1.1, 2.2.0, 2.3.0, 2.4.0, 3.0.0-3.0.2, 3.1.0, 3.2.0-3.2.4, 3.3.0-3.3.2] — no versions left
└─DiffEqFlux [aae7a2af] log: see above

5

Ehh, probably only common from those coming from MATLAB, but still worth putting in some explicit handling. I made a PR and the next release will catch this for you:

Definitely not expected. However,

Is there a reason why your Flux has to be 0.9.0?

6

Absolutely no reason why there should be any restriction to 0.9. I certainly did not do anything (conscious) to make this happen. I do not yet have enough knowledge. How does one list this restriction?
Maybe it had to do with the order with which I loaded the packages? I just tried removing Flux and reloading it, but 0.9 reloaded.

7

Can you post your ]st? And you ran ]up to make sure the package registry is up to date?

8

(v1.3) pkg> status
Status ~/.julia/environments/v1.3/Project.toml
[c52e3926] Atom v0.12.6
[0c46a032] DifferentialEquations v6.11.0
[e5e0dc1b] Juno v0.8.0
[429524aa] Optim v0.20.1
[91a5bcdd] Plots v0.29.1

I have since fixed the problem. I “activate NewProject” within Pkg, and added Flux first. I got 0.10.x
Then I added DifferentialEquations. I hope this will do the trick.

9

That’s only done once after a package updates. DifferentialEquations.jl is an especially long one, but if you only update every once in a blue moon then it’s no big deal. I think it should be added as part of the package update process. FWIW, you can call ]precompile to precompile all packages.

As for the issue, how did you run into it? I swapped the order but can’t recreate it:

(v1.3) pkg> activate Tester
Activating new environment at `D:\OneDrive\Computer\Desktop\Tester\Project.toml`

(Tester) pkg> add DifferentialEquations
 Resolving package versions...
 Installed Requires ──── v1.0.1
 Installed RecipesBase ─ v0.8.0
  Updating `D:\OneDrive\Computer\Desktop\Tester\Project.toml`
  [0c46a032] + DifferentialEquations v6.11.0
  Updating `D:\OneDrive\Computer\Desktop\Tester\Manifest.toml`
  [79e6a3ab] + Adapt v1.0.1
  [ec485272] + ArnoldiMethod v0.0.4
  [4fba245c] + ArrayInterface v2.4.1
  [4c555306] + ArrayLayouts v0.1.5
  [aae01518] + BandedMatrices v0.14.3
  [b99e7846] + BinaryProvider v0.5.8
  [764a87c0] + BoundaryValueDiffEq v2.4.0
  [d360d2e6] + ChainRulesCore v0.6.1
  [bbf7d656] + CommonSubexpressions v0.2.0
  [34da2185] + Compat v2.2.0
  [864edb3b] + DataStructures v0.17.9
  [bcd4f6db] + DelayDiffEq v5.21.0
  [2b5f629d] + DiffEqBase v6.17.3
  [459566f4] + DiffEqCallbacks v2.12.0
  [5a0ffddc] + DiffEqFinancial v2.2.1
  [c894b116] + DiffEqJump v6.5.0
  [77a26b50] + DiffEqNoiseProcess v3.9.0
  [055956cb] + DiffEqPhysics v3.5.0
  [163ba53b] + DiffResults v1.0.2
  [b552c78f] + DiffRules v1.0.1
  [0c46a032] + DifferentialEquations v6.11.0
  [c619ae07] + DimensionalPlotRecipes v1.1.0
  [b4f34e82] + Distances v0.8.2
  [ffbed154] + DocStringExtensions v0.8.1
  [d4d017d3] + ExponentialUtilities v1.6.0
  [1a297f60] + FillArrays v0.8.5
  [6a86dc24] + FiniteDiff v2.2.1
  [f6369f11] + ForwardDiff v0.10.9
  [069b7b12] + FunctionWrappers v1.0.0
  [01680d73] + GenericSVD v0.2.2
  [d25df0c9] + Inflate v0.1.1
  [42fd0dbc] + IterativeSolvers v0.8.1
  [82899510] + IteratorInterfaceExtensions v1.0.0
  [093fc24a] + LightGraphs v1.3.1
  [d3d80556] + LineSearches v7.0.1
  [1914dd2f] + MacroTools v0.5.4
  [46d2c3a1] + MuladdMacro v0.2.2
  [f9640e96] + MultiScaleArrays v1.6.0
  [d41bc354] + NLSolversBase v7.6.1
  [2774e3e8] + NLsolve v4.3.0
  [77ba4419] + NaNMath v0.3.3
  [efe28fd5] + OpenSpecFun_jll v0.5.3+1
  [bac558e1] + OrderedCollections v1.1.0
  [1dea7af3] + OrdinaryDiffEq v5.29.0
  [d96e819e] + Parameters v0.12.0
  [e409e4f3] + PoissonRandom v0.4.0
  [e6cf234a] + RandomNumbers v1.4.0
  [3cdcf5f2] + RecipesBase v0.8.0
  [731186ca] + RecursiveArrayTools v2.1.0
  [f2c3362d] + RecursiveFactorization v0.1.0
  [189a3867] + Reexport v0.2.0
  [ae029012] + Requires v1.0.1
  [ae5879a3] + ResettableStacks v1.0.0
  [f2b01f46] + Roots v0.8.4
  [699a6c99] + SimpleTraits v0.9.1
  [47a9eef4] + SparseDiffTools v1.3.3
  [276daf66] + SpecialFunctions v0.10.0
  [90137ffa] + StaticArrays v0.12.1
  [9672c7b4] + SteadyStateDiffEq v1.5.0
  [789caeaf] + StochasticDiffEq v6.19.1
  [c3572dad] + Sundials v3.8.3
  [3783bdb8] + TableTraits v1.0.0
  [a2a6695c] + TreeViews v0.3.0
  [19fa3120] + VertexSafeGraphs v0.1.1
  [700de1a5] + ZygoteRules v0.2.0
  [2a0f44e3] + Base64 
  [ade2ca70] + Dates 
  [8bb1440f] + DelimitedFiles 
  [8ba89e20] + Distributed 
  [b77e0a4c] + InteractiveUtils 
  [76f85450] + LibGit2 
  [8f399da3] + Libdl 
  [37e2e46d] + LinearAlgebra 
  [56ddb016] + Logging 
  [d6f4376e] + Markdown 
  [a63ad114] + Mmap 
  [44cfe95a] + Pkg 
  [de0858da] + Printf 
  [3fa0cd96] + REPL 
  [9a3f8284] + Random 
  [ea8e919c] + SHA 
  [9e88b42a] + Serialization 
  [1a1011a3] + SharedArrays 
  [6462fe0b] + Sockets 
  [2f01184e] + SparseArrays 
  [10745b16] + Statistics 
  [4607b0f0] + SuiteSparse 
  [8dfed614] + Test 
  [cf7118a7] + UUIDs 
  [4ec0a83e] + Unicode 

(Tester) pkg> add Flux
 Resolving package versions...
  Updating `D:\OneDrive\Computer\Desktop\Tester\Project.toml`
  [587475ba] + Flux v0.10.1
  Updating `D:\OneDrive\Computer\Desktop\Tester\Manifest.toml`
  [621f4979] + AbstractFFTs v0.5.0
  [1520ce14] + AbstractTrees v0.3.2
  [fa961155] + CEnum v0.2.0
  [3895d2a7] + CUDAapi v3.1.0
  [c5f51814] + CUDAdrv v6.0.0
  [be33ccc6] + CUDAnative v2.10.2
  [944b1d66] + CodecZlib v0.6.0
  [3da002f7] + ColorTypes v0.8.1
  [5ae59095] + Colors v0.9.6
  [3a865a2d] + CuArrays v1.7.2
  [9a962f9c] + DataAPI v1.1.0
  [7a1cc6ca] + FFTW v1.2.0
  [f5851436] + FFTW_jll v3.3.9+4
  [53c48c17] + FixedPointNumbers v0.6.1
  [587475ba] + Flux v0.10.1
  [0c68f7d7] + GPUArrays v2.0.1
  [7869d1d1] + IRTools v0.3.1
  [1d5cc7b8] + IntelOpenMP_jll v2018.0.3+0
  [e5e0dc1b] + Juno v0.7.2
  [929cbde3] + LLVM v1.3.3
  [856f044c] + MKL_jll v2019.0.117+2
  [e89f7d12] + Media v0.5.0
  [e1d29d7a] + Missings v0.4.3
  [872c559c] + NNlib v0.6.4
  [a2af1166] + SortingAlgorithms v0.3.1
  [2913bbd2] + StatsBase v0.32.1
  [a759f4b9] + TimerOutputs v0.5.3
  [3bb67fe8] + TranscodingStreams v0.9.5
  [a5390f91] + ZipFile v0.9.1
  [83775a58] + Zlib_jll v1.2.11+8
  [e88e6eb3] + Zygote v0.4.7
  [9abbd945] + Profile
10

It worked under Julia 1.3!!! I saw the learning process happen in real time. Very nice. Now I need to be able to derive the equations myself.

I had run ]up before you suggested it. Probably this contributed to my success.

I typed in the tutorial in a Julia window in Juno and copy-pasted to the REPL. Somehow, I do not think this is the preferred approach. What is the preferred approach?

Thanks for your help, Chris.

11

This video shows my package development workflow, but also just how I use Juno in general for projects. You see in there that I make heavy use of things like Ctrl + Enter to run a command in place, or Shift + Enter to run a command and then move to the next line. These Julia-specific commands are all mentioned in the Juno documentation: Basic Usage · Juno Documentation

12

I watched the video and it was quite helpful. I think I am ok for now :-). Thank you.