Analytical banded Jacobian with CVODE_BDF

[Nicholaswogan]

I am trying to use an analytical banded jacobian with CVODE_BDF. My goal is to provide CVODE_BDF with a jacobian function which returns the jacobian in band storage (not a dense matrix). It doesn't seem like this feature is available based on my post on Julialang discourse

[JianghuiDu]

Would be great to have! My current workaround is to used a sparse jacobian type with :KLU despite the jacobian being banded, which does improve performance. And I hope using a banded jacobian type with :Band it will be even better!

[JianghuiDu]

I think a function converting BandedMatrix to SUNMatrix is missing. There's already one for Matrix

function Base.convert(::Type{Matrix}, J::SUNMatrix)
    _sunmat = unsafe_load(J)
    _mat = convert(SUNMatrixContent_Dense, _sunmat.content)
    mat = unsafe_load(_mat)
    # own is false as memory is allocated by sundials
    unsafe_wrap(Array, mat.data, (mat.M, mat.N), own = false)
end

This conversion is needed here:

function cvodejac(
    t::realtype,
    u::N_Vector,
    du::N_Vector,
    J::SUNMatrix,
    funjac::AbstractFunJac{Nothing},
    tmp1::N_Vector,
    tmp2::N_Vector,
    tmp3::N_Vector,
)

    funjac.u = unsafe_wrap(Vector{Float64}, N_VGetArrayPointer_Serial(u), length(funjac.u))
    _u = funjac.u
    funjac.jac(convert(Matrix, J), _u, funjac.p, t)
    return CV_SUCCESS
end

I don't know enough to write Base.convert(::Type{BandedMatrix}, J::SUNMatrix)

[ChrisRackauckas]

You'd need to dig into the Sundials implementation of the banded matrix and figure out how to map that over to the BandedMatrices.jl version. I can't say I've looked too deeply at it either. It could be as easy as defining the Arrays directly from the pointers, or it might take an inversion or something more.