The LinearSolve.jl interface

[ChrisRackauckas]

• LinearProblem(A,b,p=SciMLBase.NullParameters();u0=nothing,kwargs...) where kwargs forward to solve
• ShiftedLinearProblem(A,b,gamma,p=SciMLBase.NullParameters();u0=nothing,kwargs...) = LinearProblem(WOperator,...)
• solve(prob,alg;reltol, abstol, weights, prec)
• cache = init(prob,alg; kwargs...) where solve = init -> solve!(cache)
• Functions on cache:
  • set_A!(cache,A)
  • set_b!(cache,b)
  • set_p!(cache,p)
  • set_prec(cache,prec)
  • update_prec!(cache) = set_prec!(cache,cache.prec(cache)...)`
• The cache should have fields A, cacheval, isfresh, pr, and pl
• The factorization alg should just have the factorization function
• IterativeSolversAlg should set the iterable to cacheval, factorization methods should store the factorized A there.
• Preconditioner functions:
  • @set cache.prec = f(Val{:init}, cache) for initialization
  • preconditioner function is f(cache) -> (pl,pr) user-defined.

Linear.pdf

[YingboMa]

Do we need ShiftedLinearProblem if there's LinearProblem(WOperator,...)?

[ChrisRackauckas]

We can leave that for us to figure out. @EdelmanJonathan won't handle that part.

[ranocha]

resize! would also be a great functionality for the cache, for example in the context of PDEs and adaptive mesh refinement.

[ChrisRackauckas]

yes, good point.

[vpuri3]

should LinearCache also have fields for present solution u, and iteration count iter (set to 0 for factorizations)?

[ChrisRackauckas]

Yes

[vpuri3]

what's weights in the third task: solve(prob,alg;reltol, abstol, weights, prec) ?

[ChrisRackauckas]

Those are the weights supposed to be used in the scaled preconditioners.