Handling sparse b with sparse A

[ytdHuang]

Hi,

I have some issues when dealing with sparse-type matrices (from package SparseArrays)

When I entered the following command, it caused an error:

julia > using SparseArrays
julia > using LinearSolve
julia > A = sprand(10, 10, 0.5)
julia > b = sprand(10, 0.5)
julia > sol = solve(LinearProblem(A , b))
ERROR: MethodError: no method matching ldiv!(::KLU.KLUFactorization{Float64, Int64}, ::SparseVector{Float64, Int64})

I've looked into the definition of ldiv! in KLU source file. The method ldiv!(::KLU.KLUFactorization{Float64, Int64}, ::SparseVector{Float64, Int64}) seems not matching ldiv!(klu::AbstractKLUFactorization{Tv}, B::StridedVecOrMat{Tv}) where {Tv<: Union{Float64, ComplexF64}}

I also tried:

julia > sol = solve(LinearProblem(A, b), LUFactorization())
ERROR: MethodError: no method matching ldiv!(::SuiteSparse.UMFPACK.UmfpackLU{Float64, Int64}, ::SparseVector{Float64, Int64})

Still not working, did I miss anything? Or should I solve sparse-type problems in different ways with LinearSolve (for example: passing custom solver in the documentation)?

Because the case I am dealing with is to solve many large sparse matrices A (the elements are all in type ComplexF64 but all A have the same sparse pattern) and b is always fixed, I really need this package.

All of my package versions are listed below

(@v1.8) pkg> status
  [ef3ab10e] KLU v0.3.0
  [ba0b0d4f] Krylov v0.8.3
  [7ed4a6bd] LinearSolve v1.26.0
  [37e2e46d] LinearAlgebra
  [2f01184e] SparseArrays

[ChrisRackauckas]

@Wimmerer what happened to all of the ldiv! methods?

[ytdHuang]

I just find out that for KLU and UmfpackLU, they only allow b::Vector{T} where T == eltype(A). They don't allow b to be SparseVector

That is, the following code works:

julia > using SparseArrays, LinearSolve
julia > A = sprand(10, 10, 0.5)
julia > b = rand(10)  # sprand is not available
julia > sol = solve(LinearProblem(A , b))

Does anyone have any idea how to solve this problem without converting the type of b from SparseVector to Vector ? Because I am dealing with the case that dimension of the Matrix is quite large (>=10,000,000). Or should I just convert b to dense Vector everytime ?

[fredrikekre]

Or should I just convert b to dense Vector everytime ?

This is usually what is done. The solution will be dense anyway, most likely.

[rayegun]

I don't believe KLU supports sparse RHS. Let me look if we have solvers that do @ChrisRackauckas

[ChrisRackauckas]

Oh, I didn't see the sparse vector part. Yeah, the solution is dense anyways so the conversion would be best. It might be good to just do that automatically?

[rayegun]

I can do that, we do a copy anyway, so I'll try to be sure we don't copy twice.