Error when Jacobian is Tridiagonal

[matthieugomez]

finite_difference_jacobian! returns an error when the Jacobian is a Tridiagonal matrix (or BandedMatrix/BlockBandedMatrix etc):

using LinearAlgebra, DiffEqDiffTools
y0 = ones(10)
J = Tridiagonal(ones(9), ones(10), ones(9))
DiffEqDiffTools.finite_difference_jacobian!(J,  (dy, y) -> dy, y0)
#> ERROR: UndefVarError: cols_index not defined

(found this when trying to use SparseDiffTools.jl for a Tridiagonal jacobian)

[ChrisRackauckas]

Interesting. I wonder if there's a generic way to do the decompression. @pkj-m let's discuss this.

[pkj-m]

I think it'll be easier to just convert all Tridiagonal (and BandedMatrices) to either a regular matrix using Convert(Array, J) or to a sparse matrix with sparse(J) before processing them further.

Tridiagonal matrices are failing this condition https://github.com/JuliaDiffEq/DiffEqDiffTools.jl/blob/master/src/jacobians.jl#L230 so they get treated as SparseMatrix which leads to the error.

[matthieugomez]

I hope that the Jacobian outputed by DiffeqDiffTools can remain Tridiagonal though (even if this particular structure is not used in finite_difference_jacobian!)

[ChrisRackauckas]

Yes, we just need to put an interface on this. rows_idxs and cols_idxs can be generic functions which we then overload for a bunch of different matrix types so they all act the same.

[pkj-m]

Yeah that sounds like a much better idea. It'll completely eliminate any extra conditions that we might have had to put on the input matrix while decompressing and probably keep the code a lot neater as well.

[ChrisRackauckas]

Think of what those interface functions need to be. We can add them to ArrayInterface.jl which is just a really lightweight "things we are looking to upstream to Base" package, and add the overloads for Base arrays there as well, with non-Base arrays using Requires.jl. Then we can use that package everywhere to introduce the right interface functions while we try to get that particular feature upstreamed to Base.

[huanglangwen]

#71
JuliaArrays/ArrayInterface.jl#9
JuliaDiff/SparseDiffTools.jl#57

[ChrisRackauckas]

Tridiagonal works now, and other structured matrices will be added by JuliaArrays/ArrayInterface.jl#14

@JuliaRegistrator register()

[JuliaRegistrator]

Registration pull request created: JuliaRegistries/General/2390

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if Julia TagBot is installed, or can be done manually through the github interface, or via:

git tag -a v1.0.0 -m "<description of version>" e06f5bfbd99f196af1798b0fbd29181923f1eb1e
git push origin v1.0.0

[matthieugomez]

That's great new! However I don't think this is working for now:

using LinearAlgebra, SparseDiffTools, DiffEqDiffTools
function f(out, x)
	for i in eachindex(x)
		out[i] = x[i] + x[max(i -1, 1)] + x[min(i+1, length(x))]
	end
	return out
end
x = rand(10)
J = Tridiagonal(ones(length(x)-1), ones(length(x)), ones(length(x)-1))
colors = matrix_colors(J)
DiffEqDiffTools.finite_difference_jacobian!(J, f, x, color=colors)
# ERROR: ArgumentError: cannot set entry (3, 1) off the tridiagonal band to a nonzero value 

[ChrisRackauckas]

The iterator for Tridiagonal might be off.

[matthieugomez]

I think there is also an issue with other types. For instance, with the master version of ArrayInterface:

using LinearAlgebra, SparseDiffTools, DiffEqDiffTools, BandedMatrices
function f(out, x)
    for i in eachindex(x)
        out[i] = x[i] + x[max(i -1, 1)] + x[min(i+1, length(x))]
    end
    return out
end
x = rand(10)
J = BandedMatrix(Zeros(length(x),length(x)), (1,1))
colors = matrix_colors(J)
DiffEqDiffTools.finite_difference_jacobian!(J, f, x, color=colors)