Using CHOLMOD.Factor as preconditionner

[tduretz]

Dear all,
I have recently tried to use Cholesky factors (of simpler problem) as a preconditionner to a Krylov solve, e.g.:

PC_fact = cholesky(PC) 
gmres!(x, A, b; Pl=PC_fact)

This fails as ldiv! is not defined for CHOLMOD.Factors:

ERROR: MethodError: no method matching ldiv!(::SparseArrays.CHOLMOD.Factor{Float64},

The issue is discussed [there] in more details (https://discourse.julialang.org/t/defining-a-preconditionner-for-iterativesolvers/86977). A temporary solution (defining ldiv! for CHOLMOD.Factors manually) is presented in that post but is there now a better approach to overcomes this?
thanks!

[tduretz]

Hi, I would like to know what are the steps needed to make this possible.
How can I help in making this happening?

In practice, I want to use this approach to solving non-symmetric systems, just like in the MWE below:

using SparseArrays, LinearAlgebra
let 
    using SparseArrays, LinearAlgebra
    let 
        # Non-symmetric matrix
        M = sparse([2 1 0 0; 1.5 3 1.5 0; 0 1 3 1; 0 0 1 2])
    
        # RHS
        b = ones(4)
    
        # Direct solve (likely LU)
        x = M\b
    
        # Alternative
        M_fact = cholesky(0.5*(M+M'))
    
        # Naive defect correction / would be better to use gmres!(...)
        x = zeros(4)
        r = zeros(4)
        for iter=1:20
            r .= M*x - b
            x .-= M_fact\r 
            @show norm(r)
        end
    end
end