Fix handling of AbstractSparseMatrixCSC

* `SciMLBase.init` did check only for `SparseMatrixCSC`, thus leading to  dispatches for AbstractSparseMatrixCSC with awful timings.
* Now, if A (resp. b) is an `AbstractSparseMatrixCSC`, instead of making a `copy` (or even `deepcopy`), a `SparseMatrixCSC` is constructed using `size`, `getcolptr`, `rowvals` and `nonzeros`.

src/common.jl

@@ -158,8 +158,10 @@ function SciMLBase.init(prob::LinearProblem, alg::SciMLLinearSolveAlgorithm,
 
     A = if alias_A || A isa SMatrix
         A
-    elseif A isa Array || A isa SparseMatrixCSC
+    elseif A isa Array
         copy(A)
+    elseif A isa AbstractSparseMatrixCSC
+        SparseMatrixCSC(size(A)..., getcolptr(A), rowvals(A), nonzeros(A))
     else
         deepcopy(A)
     end
@@ -168,8 +170,10 @@ function SciMLBase.init(prob::LinearProblem, alg::SciMLLinearSolveAlgorithm,
         Array(b) # the solution to a linear solve will always be dense!
     elseif alias_b || b isa SVector
         b
-    elseif b isa Array || b isa SparseMatrixCSC
+    elseif b isa Array
         copy(b)
+    elseif b isa AbstractSparseMatrixCSC
+        SparseMatrixCSC(size(b)..., getcolptr(b), rowvals(b), nonzeros(b))
     else
         deepcopy(b)
     end

test/basictests.jl

@@ -533,3 +533,23 @@ using BlockDiagonals
 
     @test solve(prob1, SimpleGMRES(; blocksize = 2)).u ≈ solve(prob2, SimpleGMRES()).u
 end
+
+@testset "AbstractSparseMatrixCSC" begin
+    struct MySparseMatrixCSC{Tv, Ti} <: SparseArrays.AbstractSparseMatrixCSC{Tv, Ti}
+        csc::SparseMatrixCSC{Tv, Ti}
+    end
+
+    Base.size(m::MySparseMatrixCSC) = size(m.csc)
+    SparseArrays.getcolptr(m::MySparseMatrixCSC) = SparseArrays.getcolptr(m.csc)
+    SparseArrays.rowvals(m::MySparseMatrixCSC) = SparseArrays.rowvals(m.csc)
+    SparseArrays.nonzeros(m::MySparseMatrixCSC) = SparseArrays.nonzeros(m.csc)
+
+    N = 10_000
+    A = spdiagm(1 => -ones(N - 1), 0 => fill(10.0, N), -1 => -ones(N - 1))
+    u0 = ones(size(A, 2))
+    b = A * u0
+    B = MySparseMatrixCSC(A)
+    pr = LinearProblem(B, b)
+    @time "solve MySparseMatrixCSC" u=solve(pr)
+    @test norm(u - u0, Inf) < 1.0e-13
+end