petsc version

[mpmdean]

Plan

1. Work on petsc_edrixs branch
2. First step would be to include a Krylov subspace solver using just scipy.sparse. In doing this, should manybody_operator.py be edited to be sparse? I think it should.
3. The long-term idea would be to remove all Fortran from this branch. It should be left in place in the short term for convenient testing.
4. New module called petsc_api.py should be created. This would replace pyapi.f90. This would implement functions ed_psolver, xas_psolver, rixs_psolver, opavg_psolver, which replace the existing functionsed_fsolver. I would suggest these take straight Python inputs rather than the current reading from disk.
5. Create a new file manybody_operator_petsc.py which would mirror manybody_operator.py in terms of functionality
6. Edit solvers.py where it makes calls to the Fortran. ed_fsolver, xas_fsolver, rixs_fsolver.
7. Delete scripts.py?
8. Delete iostream.py. Saving should involve either native numpy or petsc formats.
9. Change plot_spectrum.py to avoid read_poles_from_file

Questions

1. The biggest question is how to implement the two and four-fermion Hamiltonian generation for petsc (and maybe also scipy.sparse). The current Numba is a solution seems reasonable. (There would be many other options, such as Jax or conceivably Cython, c, or Mojo.) In fact, cython might be reasonably straightforward. See this example
2. Does the petsc MATSBAIJ matrix format let us skip some of the matrix setup?
3. What should the build system look like? Just Pixi?

Notes

Rubem Mondaini is knowledgable about PETSc SLEPc