CSC interface for the SPD solver

[PetrKryslUCSD]

@j-fu I started rewriting the SPD solver. I guess that means refactoring the general sparse interface.
How do you feel about that interface now? Would you change something?

[PetrKryslUCSD]

How about creating an abstract Problem, with subtypes of the detailed Problem as originally designed and a sparse-matrix based Problem?

[j-fu]

I think in a way we have this already: the CSC part just uses the SparseSolver and in that sense it is different from the part using the Sparspak Problem struct.

Essentially LinearSolve.jl provides a Problem struct for (not only) SparseMatrixCSC which among others can be solved by Sparspak.

[j-fu]

My main concerns with the architecture are:

• The _inmatrix methods have quite a bit of complex code as duplicates, and with a bit of time I would try to correct this.
• We are missing a Factorization struct (as discussed in Update csc interface #23)
• Also it seems that we could have Cholesky - great that it seems that you try to develop this! In the spirit of my remark Update csc interface #23 I then think about havin a sparspakldt . Julia also has some symmetry detection and Symmetric{A} and Hermitian{A} which can be used for some automatic detection voodoo.

Otherwise I tried to care about being drop-in compatible with other sparse solvers, and having Sparspak as a good citizen of he LinearSolve.jl backend population, and would continue to do so, as I also replaced the linear solver logic in VoronoiVFM.jl with that of LinearSolve.jl (which IMHO could be clearer, but I came to late to that party...) It works quite well and allows to be very flexible with interative/sparse solver choices.

From my POV, the Problm struct in Sparspak is quite good for teaching the steps of sparse linear solvers. I could imagine to use it for this purpose.