Decompress into a single triangle

[gdalle]

Let's see what we can do for old-school optimization solvers

[gdalle]

Here's my rough idea:

• When we get a decompression target A::SparseMatrixCSC, perform a preliminary sweep (of linear complexity) to compare it with graph.S and see whether it contains
  1. a single triangle (if so, which one)
  2. the full matrix
• During decompression, compare the result of that sweep to the uplo argument and choose the right method.
• When we get a decompression target A = Symmetric(::SparseMatrixCSC, uplo), do the same check on its parent, and choose the right method.

I can whip up a prototype implementation. My main question is what we do when the Symmetric matrix contains one triangle that makes sense and then a bunch of junk nonzeros in the other triangle. Does that ever happen? Should we error?

[amontoison]

We should error if uplo = :U or uplo = :L and decompression target A::SparseMatrixCSC contains both triangles.
We want to specialize the decompression for a given triangle.
We can vectorise the decompression for one triangle this way and support decompression in one triangle on GPU.

[amontoison]

@gdalle Do you have some bandwidth to work on that or should I try to do a draft?
It will be nice to use DI.jl in ADNLPModels.jl and it is the last missing component.

[gdalle]

Go ahead for a draft, I have zero energy and my mind is a bit foggy on what is still needed for the SMC side.