Rodas5 and ModelingToolkit much slower than Sundials' IDA on large systems

[bmetherall]

Thanks

@ChrisRackauckas

Follow the MTK tutorials.

https://mtk.sciml.ai/dev/tutorials/ode_modeling/#Symbolic-and-sparse-derivatives-1

jac=true,sparse=true creates the sparse form, and the sparsity detection is so quick that giving the sparsity pattern wouldn’t help. But if you don’t do sparse=true , it’ll create the dense Jacobian in the naïve way which won’t scale well.

Does this work with DAEs and Sundials? If I do

	prob = DAEProblem(model!, dICs, ICs, tspan, params, differential_vars = differential_vars; jac = true, sparse = true)
	@time sol = solve(prob, IDA(linear_solver = :KLU), reltol = 1e-10, abstol = 1e-6)

I get ERROR: LoadError: MethodError: no method matching nonzeros(::Nothing); it looks like the Jacobian and/or the sparsity aren’t actually being added to the problem and used. If I use the default solver, adding jac = true, sparse = true doesn’t change the timing, or allocations.