ESS scaling for the OmnigenousField class

[ddudt]

Adds the method OmnigenousField._get_ess_scale. This was omitted in #1736.

[ddudt]

The only change to this notebook was adding x_scale='ess' in the optimization.

[github-actions]

Memory benchmark result

|               Test Name                |      %Δ      |    Master (MB)     |      PR (MB)       |    Δ (MB)    |    Time PR (s)     |  Time Master (s)   |
| -------------------------------------- | ------------ | ------------------ | ------------------ | ------------ | ------------------ | ------------------ |
  test_objective_jac_w7x                 |    2.48 %    |     3.929e+03      |     4.027e+03      |    97.38     |       39.98        |       37.57        |
  test_proximal_jac_w7x_with_eq_update   |    1.39 %    |     6.441e+03      |     6.530e+03      |    89.36     |       165.02       |       164.60       |
  test_proximal_freeb_jac                |    0.11 %    |     1.315e+04      |     1.316e+04      |    14.21     |       86.24        |       85.46        |
  test_proximal_freeb_jac_blocked        |   -0.79 %    |     7.524e+03      |     7.465e+03      |    -59.13    |       75.11        |       74.11        |
  test_proximal_freeb_jac_batched        |    0.35 %    |     7.451e+03      |     7.477e+03      |    26.18     |       76.83        |       73.91        |
  test_proximal_jac_ripple               |   -1.29 %    |     3.535e+03      |     3.489e+03      |    -45.57    |       67.02        |       66.90        |
  test_proximal_jac_ripple_bounce1d      |    1.71 %    |     3.517e+03      |     3.578e+03      |    60.32     |       78.06        |       79.89        |
  test_eq_solve                          |   -0.85 %    |     2.016e+03      |     1.999e+03      |    -17.22    |       95.00        |       95.48        |

For the memory plots, go to the summary of Memory Benchmarks workflow and download the artifact.

[codecov]

Codecov Report

❌ Patch coverage is 16.66667% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.52%. Comparing base (29c7877) to head (c437b44).

Files with missing lines	Patch %	Lines
desc/magnetic_fields/_core.py	16.66%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2089      +/-   ##
==========================================
- Coverage   94.52%   94.52%   -0.01%     
==========================================
  Files         102      102              
  Lines       28785    28791       +6     
==========================================
+ Hits        27210    27214       +4     
- Misses       1575     1577       +2     

Files with missing lines	Coverage Δ
desc/magnetic_fields/_core.py	96.06% <16.66%> (-0.56%)	⬇️

... and 3 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[YigitElma]

ReviewNB

For some reason, it doesn't show my comments.

Is it normal to have such a big change in the initial trust radius? From 6.247e-02 to 6.410e-09. Because of this change, the optimization seems to start slowly, then increases the trust radius and becomes faster.

[ddudt]

ReviewNB

For some reason, it doesn't show my comments.

Is it normal to have such a big change in the initial trust radius? From 6.247e-02 to 6.410e-09. Because of this change, the optimization seems to start slowly, then increases the trust radius and becomes faster.

Interesting, I didn't realize that x_scale changes the initial_trust_radius since they are both related to the Jacobian scaling. I edited the notebook to use the "scipy" radius which is larger than the default "conngould" radius, but it still converges to the same result.