feat: add doc example for implementing the interface

[AayushSabharwal]

Close #23

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[AayushSabharwal]

Runs into

ERROR: MethodError: no method matching length(::Parameters{Vector{SubproblemParameters{Float64, Float64, Float64}}, Matrix{Float64}})
The function `length` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  length(::Base.MethodSpecializations)
   @ Base reflection.jl:1317
  length(::LLVM.VectorType)
   @ LLVM ~/.julia/packages/LLVM/joxPv/src/core/type.jl:382
  length(::DataStructures.SparseIntSet)
   @ DataStructures ~/.julia/packages/DataStructures/95DJa/src/sparse_int_set.jl:61
  ...

Stacktrace:
  [1] (::SciMLSensitivity.var"#330#339"{…})()
    @ SciMLSensitivity ~/.julia/packages/SciMLSensitivity/XCu1T/src/concrete_solve.jl:838
  [2] unthunk
    @ ~/.julia/packages/ChainRulesCore/6Pucz/src/tangent_types/thunks.jl:205 [inlined]
  [3] wrap_chainrules_output
    @ ~/.julia/packages/Zygote/NRp5C/src/compiler/chainrules.jl:110 [inlined]
  [4] map
    @ ./tuple.jl:357 [inlined]
  [5] map (repeats 3 times)
    @ ./tuple.jl:358 [inlined]
  [6] wrap_chainrules_output
    @ ~/.julia/packages/Zygote/NRp5C/src/compiler/chainrules.jl:111 [inlined]
  [7] ZBack
    @ ~/.julia/packages/Zygote/NRp5C/src/compiler/chainrules.jl:212 [inlined]
  [8] #294
    @ ~/.julia/packages/Zygote/NRp5C/src/lib/lib.jl:206 [inlined]
  [9] (::Zygote.var"#2276#back#296"{…})(Δ::ODESolution{…})
    @ Zygote ~/.julia/packages/ZygoteRules/M4xmc/src/adjoint.jl:72
 [10] #solve#51
    @ ~/.julia/packages/DiffEqBase/ODi5x/src/solve.jl:1015 [inlined]
 [11] (::Zygote.Pullback{…})(Δ::ODESolution{…})
    @ Zygote ~/.julia/packages/Zygote/NRp5C/src/compiler/interface2.jl:0
 [12] #294
    @ ~/.julia/packages/Zygote/NRp5C/src/lib/lib.jl:206 [inlined]
 [13] #2276#back
    @ ~/.julia/packages/ZygoteRules/M4xmc/src/adjoint.jl:72 [inlined]
 [14] solve
    @ ~/.julia/packages/DiffEqBase/ODi5x/src/solve.jl:1005 [inlined]
 [15] (::Zygote.Pullback{…})(Δ::ODESolution{…})
    @ Zygote ~/.julia/packages/Zygote/NRp5C/src/compiler/interface2.jl:0
 [16] #68
    @ ./REPL[58]:3 [inlined]
 [17] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Float64)
    @ Zygote ~/.julia/packages/Zygote/NRp5C/src/compiler/interface2.jl:0
 [18] (::Zygote.var"#78#79"{Zygote.Pullback{Tuple{…}, Tuple{…}}})(Δ::Float64)
    @ Zygote ~/.julia/packages/Zygote/NRp5C/src/compiler/interface.jl:91
 [19] gradient(f::Function, args::Parameters{Vector{SubproblemParameters{Float64, Float64, Float64}}, Matrix{Float64}})
    @ Zygote ~/.julia/packages/Zygote/NRp5C/src/compiler/interface.jl:148
 [20] top-level scope
    @ REPL[58]:1
Some type information was truncated. Use `show(err)` to see complete types.

[ChrisRackauckas]

@DhairyaLGandhi can you look into this?

[DhairyaLGandhi]

Yes, let me take a look

[albertomercurio]

Hello, is it possible to add an example that also includes Constants, Caches and Discrete? How do we use the repack and replace functions for any of them? Is it exactly the same as for Tunable parts?

Moreover, what if I have different Caches like a Vector and a Matrix? Should I canonicalize them as a vector? Also for the Discrete I may have many different types.

[AayushSabharwal]

is it possible to add an example that also includes Constants, Caches and Discrete?

I'll add Constants here, and mention that caches and discrete are identical.

How do we use the repack and replace functions for any of them? Is it exactly the same as for Tunable parts?

Basically yeah. repack is basically just replace. canonicalize, replace and replace! effectively agree on an implicit ordering for all elements of a portion. canonicalize takes the parameter object and outputs the array in that order. Given an array in said order, replace (replace!) creates a new parameter object (resp. writes back to the same object) assuming the array passed to it is in the correct order.

Moreover, what if I have different Caches like a Vector and a Matrix? Should I canonicalize them as a vector?

Yes, they need to be flattened and concatenated.

Also for the Discrete I may have many different types.

They need to be concatenated into one type-unstable array

[ChrisRackauckas]

What's left here?

[AayushSabharwal]

I have the doc changes ready, SciMLSensitivity needs a tag

[ChrisRackauckas]

All of the SciMLStructures changes that were ready were tagged last week?

[ChrisRackauckas]

🎉