Performance Regression from SparseDiffTools: Specialized sparse matrix decompression for structured matrices

[ChrisRackauckas]

Using a fallback to sparse matrices for many applications can be a major slowdown, and thus structured matrices are used. However, DI does not seem to be compatible with the full gambit.

In particular, DI can be a bit slow because it's missing the use of analytical coloring solutions and faster iteration strategies on structured matrices:

• https://github.com/JuliaArrays/ArrayInterface.jl/blob/master/ext/ArrayInterfaceBandedMatricesExt.jl
• https://github.com/JuliaArrays/ArrayInterface.jl/blob/master/ext/ArrayInterfaceBlockBandedMatricesExt.jl#L207-L244
• https://github.com/JuliaDiff/FiniteDiff.jl/blob/master/ext/FiniteDiffBlockBandedMatricesExt.jl#L16-L68
• https://github.com/JuliaDiff/FiniteDiff.jl/blob/master/ext/FiniteDiffBandedMatricesExt.jl#L13-L27

It would be good if these can be adopted into the DI style so that the full performance on non-SparseMatrixCSC sparse matrices can be recovered.

[gdalle]

We're aware of this request, and there are two issues open on the SparseMatrixColorings side to track progress:

• Optimized coloring for specific matrix types gdalle/SparseMatrixColorings.jl#65
• Optimized decompression for specific matrix types gdalle/SparseMatrixColorings.jl#64

Since this aspect is totally independent from DI, I'm gonna close the current issue. However, I would be interested if you can cook up an MWE with a measurable difference in speed between SparseDiffTools and DI+SMC. If you find one, please put it in gdalle/SparseMatrixColorings.jl#64