Utility functions for initializing coils for stage 2 optimization

[f0uriest]

Resolves #1182
Resolves #1183

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.69%. Comparing base (ccf72cb) to head (dcf666c).
Report is 25 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1361      +/-   ##
==========================================
- Coverage   95.69%   95.69%   -0.01%     
==========================================
  Files         101      101              
  Lines       25569    25601      +32     
==========================================
+ Hits        24468    24498      +30     
- Misses       1101     1103       +2     

Files with missing lines	Coverage Δ
desc/coils.py	98.07% <100.00%> (+0.08%)	⬆️

... and 2 files with indirect coverage changes

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     -0.82 +/- 4.56     | -4.52e-03 +/- 2.52e-02 |  5.47e-01 +/- 2.4e-02  |  5.52e-01 +/- 8.7e-03  |
 test_equilibrium_init_medres            |     -1.06 +/- 4.65     | -4.60e-02 +/- 2.02e-01 |  4.29e+00 +/- 6.0e-02  |  4.33e+00 +/- 1.9e-01  |
 test_equilibrium_init_highres           |     +2.85 +/- 1.30     | +1.55e-01 +/- 7.09e-02 |  5.59e+00 +/- 4.0e-02  |  5.44e+00 +/- 5.9e-02  |
 test_objective_compile_dshape_current   |     +1.06 +/- 1.51     | +4.18e-02 +/- 5.93e-02 |  3.98e+00 +/- 4.6e-02  |  3.94e+00 +/- 3.7e-02  |
 test_objective_compute_dshape_current   |     +1.53 +/- 2.30     | +7.97e-05 +/- 1.19e-04 |  5.28e-03 +/- 7.2e-05  |  5.20e-03 +/- 9.6e-05  |
 test_objective_jac_dshape_current       |     +1.83 +/- 6.79     | +7.84e-04 +/- 2.92e-03 |  4.37e-02 +/- 2.6e-03  |  4.29e-02 +/- 1.3e-03  |
 test_perturb_2                          |     +2.48 +/- 2.66     | +4.88e-01 +/- 5.23e-01 |  2.02e+01 +/- 4.3e-01  |  1.97e+01 +/- 3.0e-01  |
 test_proximal_freeb_jac                 |     +0.50 +/- 1.35     | +3.73e-02 +/- 1.01e-01 |  7.47e+00 +/- 9.5e-02  |  7.44e+00 +/- 3.4e-02  |
 test_solve_fixed_iter                   |     +1.44 +/- 1.84     | +4.66e-01 +/- 5.93e-01 |  3.27e+01 +/- 4.9e-01  |  3.23e+01 +/- 3.4e-01  |
 test_LinearConstraintProjection_build   |     +1.77 +/- 3.30     | +1.84e-01 +/- 3.43e-01 |  1.06e+01 +/- 2.1e-01  |  1.04e+01 +/- 2.7e-01  |
 test_build_transform_fft_midres         |     +3.19 +/- 5.09     | +1.87e-02 +/- 2.99e-02 |  6.05e-01 +/- 2.6e-02  |  5.87e-01 +/- 1.5e-02  |
 test_build_transform_fft_highres        |     +4.77 +/- 4.11     | +4.47e-02 +/- 3.85e-02 |  9.82e-01 +/- 3.0e-02  |  9.37e-01 +/- 2.4e-02  |
 test_equilibrium_init_lowres            |     +6.75 +/- 4.35     | +2.49e-01 +/- 1.60e-01 |  3.93e+00 +/- 1.6e-01  |  3.68e+00 +/- 3.2e-02  |
 test_objective_compile_atf              |     +3.62 +/- 2.28     | +2.83e-01 +/- 1.79e-01 |  8.11e+00 +/- 6.7e-02  |  7.82e+00 +/- 1.7e-01  |
 test_objective_compute_atf              |     +8.62 +/- 3.14     | +1.29e-03 +/- 4.69e-04 |  1.62e-02 +/- 3.7e-04  |  1.49e-02 +/- 2.9e-04  |
 test_objective_jac_atf                  |     +5.24 +/- 3.61     | +9.92e-02 +/- 6.82e-02 |  1.99e+00 +/- 3.9e-02  |  1.89e+00 +/- 5.6e-02  |
 test_perturb_1                          |     +3.60 +/- 3.06     | +5.16e-01 +/- 4.39e-01 |  1.49e+01 +/- 4.3e-01  |  1.43e+01 +/- 8.6e-02  |
 test_proximal_jac_atf                   |     +0.61 +/- 1.14     | +5.03e-02 +/- 9.37e-02 |  8.29e+00 +/- 7.6e-02  |  8.24e+00 +/- 5.5e-02  |
 test_proximal_freeb_compute             |     +5.20 +/- 3.48     | +9.87e-03 +/- 6.61e-03 |  2.00e-01 +/- 2.8e-03  |  1.90e-01 +/- 6.0e-03  |
 test_solve_fixed_iter_compiled          |     +3.98 +/- 2.37     | +7.77e-01 +/- 4.62e-01 |  2.03e+01 +/- 4.3e-01  |  1.95e+01 +/- 1.7e-01  |

[dpanici]

I think some of the outer saddle coils are linking the modular coils for the finite beta example

[f0uriest]

Can someone try running the updated notebook locally? The test is failing but everything seems fine locally for me.

[dpanici]

Can someone try running the updated notebook locally? The test is failing but everything seems fine locally for me.

I also ran locally with no issues. Maybe a memory issue with the CI runner, related to the linking number objective?

[dpanici]

I merged the notebook with master, it should be good now

[f0uriest]

I merged the notebook with master, it should be good now

Did you also re-run it? Or just merge the old version? I don't think the previous one included all the recent changes

[dpanici]

@dpanici rerun this

[dpanici]

rerun notebook

[sinaatalay]

Two functions have been added to desc.coils (initialize_modular_coils and initialize_saddle_coils), and their tests have been written. I couldn't find any spelling errors in docs/docstrings. I don't fully understand what's happening inside the functions, but their tests seem reliable to me, and they pass. I think's this PR is good to go.