Programmatic way to obtain the Jacobian function

[Datseris]

Question❓

With things in MTK changing, it is a bad idea to rely on internals. Indeed, in DynamicalSystems.jl we attempt to extract a symbolic/generated Jacobian if the system is a result of an MTK build. Originally we were doing:

if prob.f isa SciMLBase.AbstractDiffEqFunction && !isnothing(prob.f.jac)
            J = prob.f.jac

but this no longer works. Is there already, or can you add if not, a programmatic way (API function) to obtain the Jacobian function J so that one can call J(u, p, t) (or J!(J0, u, p, t) for inplace)?

[vyudu]

Yes, there is generate_jacobian

[ChrisRackauckas]

Yeah we need to fix up the multi-docstring thing, but generate_jacobian is the function for it. The rest of this issue is the doc overhaul as if the docstrings showed up this would have been clear #3505

[Datseris]

Thanks. Does generate_jacobian take into account in-place or out-of-place-ness? I found its docstring here: https://docs.sciml.ai/ModelingToolkit/stable/systems/NonlinearSystem/#ModelingToolkit.generate_jacobian-systems-NonlinearSystem but it doesn't mention anything for that.

[ChrisRackauckas]

All of the function generators generate both as a tuple.

[Datseris]

I am not sure how to use the generate_jacobian function. It does not return functions, but rather Expr objects:

Joop, Jiip = generate_jacobian(model)
(:(function (__mtk_arg_1, ___mtkparameters___, t)
      #= C:\Users\datse\.julia\packages\Symbolics\y6jSx\src\build_function.jl:366 =# @inbounds begin
              #= C:\Users\datse\.julia\packages\Symbolics\y6jSx\src\build_function.jl:366 =#
              begin
                  #= C:\Users\datse\.julia\packages\SymbolicUtils\MGDe2\src\code.jl:409 =#
                  #= C:\Users\datse\.julia\packages\SymbolicUtils\MGDe2\src\code.jl:410 =#
                  #= C:\Users\datse\.julia\packages\SymbolicUtils\MGDe2\src\code.jl:411 =#
                  begin
                      __mtk_arg_2 = ___mtkparameters___[1]
                      begin
                          var"##cse#1" = (view)(__mtk_arg_1, 1:2)
                          var"##cse#2" = (reshape)(var"##cse#1", (2,))
                          var"u(t)" = var"##cse#2"
                          var"##cse#3" = (view)(__mtk_arg_2, 1:2)
                          var"##cse#4" = (reshape)(var"##cse#3", (2,))
                          var"Initial(u(t))" = var"##cse#4"
                          begin
                              #= C:\Users\datse\.julia\packages\SymbolicUtils\MGDe2\src\code.jl:510 =#
                              (SymbolicUtils.Code.create_array)(typeof(__mtk_arg_1), nothing, Val{2}(), Val{(2, 2)}(), 3.0, 0, 0, -3.0)
                          end
....

How do I convert these to callable functions? Do I have to call @eval first on them to generate the function (which appears odd, I would be doing @eval inside a dynamical systems function)?

[Datseris]

Right, got it, I have to pass expression = Val{false} as a keyword, which creates the generated function object.