Fix SplitFunction to use user-provided jvp function

When a user provides a jvp function to SplitFunction, it should be used
instead of falling back to automatic differentiation. The has_jvp check
was only checking f.f1 instead of first checking the SplitFunction's
own jvp field.

This fix checks the SplitFunction's own fields (jvp, vjp, jac, etc.)
first before delegating to f.f1, which allows user-provided analytical
derivatives to be used properly with matrix-free Krylov solvers.

Fixes SciML/DifferentialEquations.jl#1109

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

src/scimlfunctions.jl

@@ -5046,15 +5046,15 @@ function has_observed(f::AbstractSciMLFunction)
 end
 has_colorvec(f::AbstractSciMLFunction) = __has_colorvec(f) && f.colorvec !== nothing
 
-# TODO: find an appropriate way to check `has_*`
-has_jac(f::Union{SplitFunction, SplitSDEFunction}) = has_jac(f.f1)
-has_jvp(f::Union{SplitFunction, SplitSDEFunction}) = has_jvp(f.f1)
-has_vjp(f::Union{SplitFunction, SplitSDEFunction}) = has_vjp(f.f1)
-has_tgrad(f::Union{SplitFunction, SplitSDEFunction}) = has_tgrad(f.f1)
-has_Wfact(f::Union{SplitFunction, SplitSDEFunction}) = has_Wfact(f.f1)
-has_Wfact_t(f::Union{SplitFunction, SplitSDEFunction}) = has_Wfact_t(f.f1)
-has_paramjac(f::Union{SplitFunction, SplitSDEFunction}) = has_paramjac(f.f1)
-has_colorvec(f::Union{SplitFunction, SplitSDEFunction}) = has_colorvec(f.f1)
+# Check the SplitFunction's own fields first before delegating to f.f1
+has_jac(f::Union{SplitFunction, SplitSDEFunction}) = (__has_jac(f) && f.jac !== nothing) || has_jac(f.f1)
+has_jvp(f::Union{SplitFunction, SplitSDEFunction}) = (__has_jvp(f) && f.jvp !== nothing) || has_jvp(f.f1)
+has_vjp(f::Union{SplitFunction, SplitSDEFunction}) = (__has_vjp(f) && f.vjp !== nothing) || has_vjp(f.f1)
+has_tgrad(f::Union{SplitFunction, SplitSDEFunction}) = (__has_tgrad(f) && f.tgrad !== nothing) || has_tgrad(f.f1)
+has_Wfact(f::Union{SplitFunction, SplitSDEFunction}) = (__has_Wfact(f) && f.Wfact !== nothing) || has_Wfact(f.f1)
+has_Wfact_t(f::Union{SplitFunction, SplitSDEFunction}) = (__has_Wfact_t(f) && f.Wfact_t !== nothing) || has_Wfact_t(f.f1)
+has_paramjac(f::Union{SplitFunction, SplitSDEFunction}) = (__has_paramjac(f) && f.paramjac !== nothing) || has_paramjac(f.f1)
+has_colorvec(f::Union{SplitFunction, SplitSDEFunction}) = (__has_colorvec(f) && f.colorvec !== nothing) || has_colorvec(f.f1)
 
 has_jac(f::Union{DynamicalODEFunction, DynamicalDDEFunction}) = has_jac(f.f1)
 has_jvp(f::Union{DynamicalODEFunction, DynamicalDDEFunction}) = has_jvp(f.f1)