Encoding prior knowledge for the solution of linear systems

[JonathanWenger]

Is your feature request related to a problem? Please describe.
Currently it is not always clear how a user can supply prior knowledge to the probabilistic linear solver via a prior belief over the inverse / solution and matrix.

Give an example use case.
Say the user has knowledge about the spectrum, smallest eigenvalue of A or a preconditioner. Currently it is not clear how this should be encoded into a prior belief.

# Known spectrum of A

# Prior belief
belief = LinearSystemBelief.from_spectrum(spectrum)
belief = LinearSystemBelief.from_preconditioner(spectrum)
belief = LinearSystemBelief.from_min_eigenvalue(spectrum)

Describe the solution you'd like.
Provide specific prior belief classes with constructors from_* which cover the most common use cases of encoding prior knowledge.

[mmahsereci]

Thanks, Jonathan, I think this is an important issue. I have two questions:

• Are there best practices known for certain settings? For example if I have the spectrum, which of the three examples mentioned above is best to choose? Is there an automated way to choose?
• The change may also involve changing the UI of problinsolve, doesn't it?