Should iterative refinement be opt-in?

[ViralBShah]

It seems like iterative refinement is the default.

Pardiso.jl/src/Pardiso.jl

Line 242 in 81c8391

set_phase!(ps, ANALYSIS_NUM_FACT_SOLVE_REFINE)

Discussion on iterative refinement for Julia sparse solvers:
https://github.com/JuliaLang/julia/issues/31105#issuecomment-465030232

cc @andreasnoack

[ViralBShah]

cc @ranjanan

[ranjanan]

According to https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-fortran/top/sparse-solver-routines/onemkl-pardiso-parallel-direct-sparse-solver-interface/onemkl-pardiso-parameters-in-tabular-form.html, it looks like 23 corresponds to just factorization + solve? Only 33 is iterative refinement.

[ViralBShah]

It seems that the intel table that @ranjanan links above is not consistent with pardiso params.

According to the pardiso params, parameter 13 is Analysis, numerical factorization, solve, iterative refinement. In fact, I can't quite tell if there is an easy way to solve without refinement.

[j-fu]

Just my 2ct: yes, iterative refinement should be opt-in. May be we want to do e.g. iterative
refinement with IterativeSolvers, or the solution is part of a bigger block preconditioner...

With pardiso, setting iparm[8]=0 should prevent iterative refinement unless pivot perturbation was activated.