Yet another single-stage refactor

[landreman]

This is yet another possible refactoring of the single-stage example in #301 suggested by @mbkumar, as an alternative to #317. In this approach, MPIFiniteDifference broadcasts full_x instead of just the free x, so there is no extra data that needs to be broadcast. The coil dofs are fixed during the finite-differencing, then un-fixed to update the coil dofs and compute their gradient analytically, then fixed again for the next finite-differencing, etc. Even though the coil dofs are fixed during the finite differencing, they are still part of full_x, so they get broadcast.

To get this working, a few functions were added to Optimizable: a setter for full_x (copied from @mbkumar 's commit to #317), and full_fix() and full_unfix() to set the free/fixed property for the full dofs on which an object depends. Corresponding tests have been added. A few changes from #301 to finite_difference.py and optimizable.py have been reverted, as in #317.

For single_stage_optimization_finite_beta.py, this branch gives identical values for all quantities at the end of the optimization and uses fewer calls to VirtualCasing.from_vmec() compared to #301.

I don't have a super strong preference between this approach and #317, but perhaps slightly prefer this one, since it makes sense that full_x should be synched by MPIFiniteDifference anyway. What do you think?

[codecov]

Codecov Report

Patch coverage: 100.00% and project coverage change: -0.40 ⚠️

Comparison is base (dbf0232) 90.78% compared to head (7dfa31d) 90.38%.

Additional details and impacted files

@@                  Coverage Diff                   @@
##           rj/single_stage_PR     #319      +/-   ##
======================================================
- Coverage               90.78%   90.38%   -0.40%     
======================================================
  Files                      63       63              
  Lines                   10719    10732      +13     
======================================================
- Hits                     9731     9700      -31     
- Misses                    988     1032      +44     

Flag	Coverage Δ
unittests	90.38% <100.00%> (-0.40%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/simsopt/_core/finite_difference.py	93.22% <100.00%> (-0.88%)	⬇️
src/simsopt/_core/optimizable.py	90.35% <100.00%> (+0.18%)	⬆️

... and 9 files with indirect coverage changes

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