Add initial_guess parameter to apply_inverse

[sdrave]

and apply_inverse_adjoint.

It is used in the following places:

• Operator.apply_inverse passes initial_guess to newton in case of a nonlinear operator.
• Generic lgmres, as well as SciPy bicgstab, lgmres, lsmr, lsqr.
• The FEniCS bindings pass initial_guess to the backend.
• implicit_euler sets initial_guess to the solution of the last time step.

Fixes #924.

[pmli]

Looks good to me.
I'm just wondering, since it helps with instationary models, could/should the initial_guess also be passed to stationary models?

[codecov]

Codecov Report

Merging #941 into master will decrease coverage by 0.57%.
The diff coverage is 88.79%.

Impacted Files	Coverage Δ
src/pymor/operators/mpi.py	17.56% <50.00%> (-0.25%)	⬇️
src/pymor/operators/list.py	64.35% <77.77%> (+0.35%)	⬆️
src/pymor/operators/block.py	83.88% <85.71%> (-0.51%)	⬇️
src/pymor/operators/numpy.py	78.60% <85.71%> (+0.10%)	⬆️
src/pymor/operators/constructions.py	83.89% <90.47%> (+0.13%)	⬆️
src/pymor/algorithms/genericsolvers.py	78.35% <100.00%> (+0.08%)	⬆️
src/pymor/algorithms/timestepping.py	78.18% <100.00%> (ø)
src/pymor/bindings/fenics.py	81.57% <100.00%> (ø)
src/pymor/bindings/ngsolve.py	85.29% <100.00%> (ø)
src/pymor/bindings/pyamg.py	86.36% <100.00%> (+0.31%)	⬆️
... and 3 more

[sdrave]

I'm just wondering, since it helps with instationary models, could/should the initial_guess also be passed to stationary models?

But how to choose an initial guess for the stationary case?

[pmli]

I guess this is something only the user could provide. My question is how to give this possibility to the user. (I admit it's kind of a different issue from adding initial_guess to apply_inverse.)

[sdrave]

I guess this is something only the user could provide. My question is how to give this possibility to the user. (I admit it's kind of a different issue from adding initial_guess to apply_inverse.)

I think it should be the job of the Model to set an adequate initial guess if needed. It is not hard to subclass StationaryModel and implement your own _solve. It would also be imaginable to extend StationaryModel with an additional __init__ argument or an initial_guess method. But before doing so, I would like to have a user who has a need for it.

[pmli]

Ok, sounds good.