[later] pair fwd and bwd operators

[vpuri3]

If you have access to a cheap inverse for an operator, A, then it would be very convenient to use that for LinearAlgebra.ldiv!, Base.\.

Trivial example: ldiv! with diagonal is ~15x slower than mul!.

julia> n=1024;

julia> u=rand(n); v=copy(u); D=Diagonal(copy(u));

julia> @btime mul!($v,$D,$u);
  129.625 ns (0 allocations: 0 bytes)

julia> @btime ldiv!($v,$D,$u);
  2.030 μs (0 allocations: 0 bytes)

This will also be useful for passing jac to SplitFunction. Maybe this could help CliMA/ClimaCore.jl#41 not sure.

I propose extending InvertibleOperator as follows:

struct InvertibleOperator
    A # fwd SciMLOperator
    F # inv
end

where F can be the inverse (SciML)Operator, or any object with 3 arg mul!, * defined.

[gaurav-arya]

If we have a cheap inverse of A, we nearly always have a cheap inverse of A + kI, so the design should accomodate that case too

[vpuri3]

we can create a new type for that and Sherman Morrison formula

[vpuri3]

@gaurav-arya do you wanna create a new issue for #84 (comment) with a design idea?

[gaurav-arya]

Just did: #180