Add L-BFGS reconstruction engine

[jfowkes]

Resurrecting #400 as GitHub broke the original PR.

Add Limited-memory BFGS reconstruction engine to as an alternative to ML.

Caveats:

• L-BFGS does not support the object smoothing preconditioner for technical reasons (this would require the ability to invert the Gaussian filter, i.e. exactly de-blur and this is known to be impossible). However probe preconditioning (i.e. probe-object scaling) is supported and this is enough to reconstruct on the moonflower example with a lower error than ML.

[jfowkes]

@daurer this L-BFGS pull request is now ready for review and potential merge.

[daurer]

Needs a CuPy engine before it can be merged. @ptim0626 maybe something for you?

[ptim0626]

A quick comment, the tolerance for LBFGS's tests is increased as it is very likely the discrepancy is a result of numerical instability instead of the problem of implementation.

[jfowkes]

@daurer this PR will soon need to be updated to use the wavefield preconditioner, I'm happy to do this.

[jfowkes]

@daurer I've now added the wavefield preconditioner to LBFGS with tests and templates. Unfortunately pytest has stopped picking up the LBFGS tests in the CI, I assume this is the same issue that we had with the ML engine tests not being picked up?

[daurer]

@daurer I've now added the wavefield preconditioner to LBFGS with tests and templates. Unfortunately pytest has stopped picking up the LBFGS tests in the CI, I assume this is the same issue that we had with the ML engine tests not being picked up?

just saw this comment now. I think the tests should be name <something>_test.py

[jfowkes]

just saw this comment now. I think the tests should be name <something>_test.py

Done. All tests now running (aside from the serial wavefield caveat as in #607) and passing.