Utility functions for initializing coils for stage 2 optimization

[f0uriest]

Resolves #1182
Resolves #1183

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.51%. Comparing base (df95b90) to head (c576392).
Report is 2 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1361   +/-   ##
=======================================
  Coverage   95.51%   95.51%           
=======================================
  Files          96       96           
  Lines       24047    24080   +33     
=======================================
+ Hits        22969    23001   +32     
- Misses       1078     1079    +1     

Files with missing lines	Coverage Δ
desc/coils.py	97.59% <100.00%> (+0.11%)	⬆️

... and 2 files with indirect coverage changes

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_midres         |     -1.32 +/- 7.85     | -8.34e-03 +/- 4.97e-02 |  6.24e-01 +/- 2.7e-02  |  6.32e-01 +/- 4.2e-02  |
 test_build_transform_fft_highres        |     -3.21 +/- 6.00     | -3.38e-02 +/- 6.32e-02 |  1.02e+00 +/- 5.3e-02  |  1.05e+00 +/- 3.4e-02  |
 test_equilibrium_init_lowres            |     -1.13 +/- 4.23     | -4.41e-02 +/- 1.65e-01 |  3.85e+00 +/- 9.8e-02  |  3.89e+00 +/- 1.3e-01  |
 test_objective_compile_atf              |     +0.58 +/- 4.88     | +4.56e-02 +/- 3.83e-01 |  7.91e+00 +/- 3.3e-01  |  7.86e+00 +/- 2.0e-01  |
 test_objective_compute_atf              |     -0.39 +/- 2.22     | -4.21e-05 +/- 2.38e-04 |  1.07e-02 +/- 1.2e-04  |  1.07e-02 +/- 2.1e-04  |
 test_objective_jac_atf                  |     -4.60 +/- 4.56     | -9.11e-02 +/- 9.04e-02 |  1.89e+00 +/- 7.0e-02  |  1.98e+00 +/- 5.7e-02  |
 test_perturb_1                          |     +2.02 +/- 3.96     | +2.59e-01 +/- 5.08e-01 |  1.31e+01 +/- 3.8e-01  |  1.28e+01 +/- 3.3e-01  |
 test_proximal_jac_atf                   |     +0.44 +/- 1.02     | +3.64e-02 +/- 8.41e-02 |  8.25e+00 +/- 3.9e-02  |  8.21e+00 +/- 7.4e-02  |
 test_proximal_freeb_compute             |     +2.47 +/- 1.33     | +4.50e-03 +/- 2.41e-03 |  1.86e-01 +/- 1.9e-03  |  1.82e-01 +/- 1.5e-03  |
 test_build_transform_fft_lowres         |     +0.45 +/- 2.30     | +2.34e-03 +/- 1.19e-02 |  5.19e-01 +/- 7.9e-03  |  5.17e-01 +/- 8.8e-03  |
 test_equilibrium_init_medres            |     -0.38 +/- 1.09     | -1.54e-02 +/- 4.47e-02 |  4.08e+00 +/- 2.7e-02  |  4.09e+00 +/- 3.6e-02  |
 test_equilibrium_init_highres           |     -0.20 +/- 0.69     | -1.08e-02 +/- 3.75e-02 |  5.44e+00 +/- 2.8e-02  |  5.45e+00 +/- 2.5e-02  |
 test_objective_compile_dshape_current   |     -0.47 +/- 1.58     | -1.80e-02 +/- 6.04e-02 |  3.81e+00 +/- 1.8e-02  |  3.83e+00 +/- 5.8e-02  |
 test_objective_compute_dshape_current   |     +0.05 +/- 1.70     | +1.99e-06 +/- 6.17e-05 |  3.63e-03 +/- 4.7e-05  |  3.63e-03 +/- 4.0e-05  |
 test_objective_jac_dshape_current       |     -7.63 +/- 4.46     | -3.22e-03 +/- 1.88e-03 |  3.90e-02 +/- 1.4e-03  |  4.23e-02 +/- 1.2e-03  |
 test_perturb_2                          |     -1.72 +/- 6.80     | -3.05e-01 +/- 1.21e+00 |  1.75e+01 +/- 1.2e-01  |  1.78e+01 +/- 1.2e+00  |
 test_proximal_freeb_jac                 |     -0.21 +/- 1.11     | -1.56e-02 +/- 8.23e-02 |  7.40e+00 +/- 4.0e-02  |  7.42e+00 +/- 7.2e-02  |
 test_solve_fixed_iter                   |     +0.26 +/- 59.89    | +1.30e-02 +/- 3.01e+00 |  5.04e+00 +/- 2.1e+00  |  5.03e+00 +/- 2.2e+00  |

[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?