Refactor LinearOperator for method overriding

[timweiland]

In a Nutshell

_matmul, _apply, _transpose etc. can now be implemented by overriding the corresponding methods in a subclass instead of passing the implementations in the constructor. The previous approach is still possible via the new LambdaLinearOperator.

Detailed Description

• Refactor LinearOperator such that method implementations are provided via subclass overrides
• Introduce LambdaLinearOperator subclass which provides support for the old approach of passing method implementations via the constructor
• Replace all previous uses of LinearOperator with LambdaLinearOperator to maintain compatibility

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[marvinpfoertner]

Thanks for taking care of this! 🙏🏻

Some general points:

• Instead of just saying "You may implement this method in a subclass.", we should probably state that overriding the default implementation only makes sense if we know a more efficient implementation (in terms of memory or computation time) than the fallback.
• Can you get rid of the double underscores in the cache variables? We don't really need those anymore

[codecov]

Codecov Report

Merging #735 (ae8b0dc) into main (3999850) will increase coverage by 0.13%.
The diff coverage is 98.12%.

@@            Coverage Diff             @@
##             main     #735      +/-   ##
==========================================
+ Coverage   90.27%   90.40%   +0.13%     
==========================================
  Files         197      197              
  Lines        7445     7454       +9     
  Branches      989      966      -23     
==========================================
+ Hits         6721     6739      +18     
+ Misses        487      481       -6     
+ Partials      237      234       -3     

Impacted Files	Coverage Δ
src/probnum/linops/_utils.py	69.23% <0.00%> (ø)
src/probnum/linops/_linear_operator.py	88.05% <98.56%> (+2.13%)	⬆️
src/probnum/linalg/solvers/matrixbased.py	73.75% <100.00%> (ø)
src/probnum/linops/__init__.py	100.00% <100.00%> (ø)
src/probnum/linops/_arithmetic_fallbacks.py	85.57% <100.00%> (ø)
src/probnum/linops/_kronecker.py	89.80% <100.00%> (-0.91%)	⬇️
src/probnum/linops/_scaling.py	82.73% <100.00%> (+0.17%)	⬆️

[JonathanWenger]

Great job on your first PR @timweiland. To fix the formatting and isort issues, once you've installed tox you can run

tox -e format

To automatically keep code formatted you can also install the formatting libraries directly via

cd probnum
pip install -r formatting-requirements

You can then run black and isort on save in VSCode for example. To avoid comitting files which are incorrectly formatted in the future you can also alternatively install the provided precommit hooks to check for correct formatting prior to comitting (see https://probnum.readthedocs.io/en/latest/development/pull_request.html#pre-commit-hooks)

[timweiland]

Thanks @JonathanWenger! I've fixed all of the problems now except for one which I'm unsure about:
Pylint complains that in this code, self.T is not callable (E1102): y = (self.T)(x, axis=-1)
But clearly, self.T returns a LinearOperator which is callable: def T(self) -> "LinearOperator":
Do you know how to fix this? It seems that it might have something to do with the @property decorator.

[timweiland]

Thanks @JonathanWenger! I've fixed all of the problems now except for one which I'm unsure about: Pylint complains that in this code, self.T is not callable (E1102): y = (self.T)(x, axis=-1) But clearly, self.T returns a LinearOperator which is callable: def T(self) -> "LinearOperator": Do you know how to fix this? It seems that it might have something to do with the @property decorator.

I talked to @marvinpfoertner about this and we agreed to simply make pylint ignore this line.

[marvinpfoertner]

Thanks again for doing this! :) Congrats on you first ProbNum PR! 🎉