More general \ and ldiv! for incomplete Cholesky

[JeffFessler]

The diagonal preconditioner has a general ldiv! method that can apply to a vector or a matrix because b is duck typed:

Preconditioners.jl/src/diagonal.jl

Line 40 in 52b3702

ldiv!(C::DiagonalPreconditioner, b) = ldiv!(b, C, b)

In contrast, the incomplete Cholesky preconditioner ldiv! is pinned to a Vector argument:

Preconditioners.jl/src/incompletecholesky.jl

Line 28 in 52b3702

@inline function ldiv!(y::AbstractVector, C::CholeskyPreconditioner, b::AbstractVector)

Could the package provide a more general RHS? Something like:

@inline function ldiv!(y::AbstractVecOrMat, C::CholeskyPreconditioner, b::AbstractVecOrMat)

One related hack is something like this:

import Base.\
\(C::CholeskyPreconditioner, A::AbstractMatrix) = reduce(hcat, [C \ c for c in eachcol(A)])

but I think there should be a better way?

[mohamed82008]

We will need to upstream these implementations to the dependency packages first if possible. If the maintainers are not receptive, we can roll our own implementation here.