feat: compute jac_prototype for SDEFunction

[vyudu]

Close #3527

[ChrisRackauckas]

Can we make sure to add the mass matrix into the pattern? Because it will be a requirement of the future, so we should just make it robust now.

[vyudu]

Mass matrix is already in there

[ChrisRackauckas]

The mass matrix is a subset of jacobian_sparsity(sys)? Are you sure? I don't remember handling that here.

[vyudu]

No I mean it was there before, see lines 656-657 of the updated file

[vyudu]

@ChrisRackauckas @oscardssmith @AayushSabharwal
So the behavior implemented here is:

• generate_jacobian returns the jacobian, generate_W returns the W
• prob.f.jac_prototype and prob.f.W_prototype both return the same thing, the W_prototype (which I added in case we want to switch to only using W_prototype in the solvers at some point)
• the jac! returned by generate_jacobian will error if the passed in jac doesn't have the W pattern

is this right? anything I'm missing?

[vyudu]

Nevermind this is writing to the wrong entries, need to investigate

JuliaSymbolics/Symbolics.jl#1521

[ChrisRackauckas]

So this is good to go?

[vyudu]

No I think it's still writing to the wrong entries sorry, investigating

[vyudu]

OK I think I fixed it, let's see how tests do.

[vyudu]

@ChrisRackauckas