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 95.61%. Comparing base (34dbac0) to head (c06b995).

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1361   +/-   ##
=======================================
  Coverage   95.60%   95.61%           
=======================================
  Files          98       98           
  Lines       25417    25450   +33     
=======================================
+ Hits        24300    24334   +34     
+ Misses       1117     1116    -1     

Files with missing lines	Coverage Δ
desc/coils.py	98.07% <100.00%> (+0.09%)	⬆️

... and 1 file with indirect coverage changes

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     -6.16 +/- 5.89     | -3.57e-02 +/- 3.42e-02 |  5.44e-01 +/- 3.1e-02  |  5.80e-01 +/- 1.4e-02  |
+test_equilibrium_init_medres            |    -10.18 +/- 2.59     | -4.68e-01 +/- 1.19e-01 |  4.13e+00 +/- 1.0e-01  |  4.60e+00 +/- 6.1e-02  |
 test_equilibrium_init_highres           |     -6.64 +/- 2.78     | -3.85e-01 +/- 1.61e-01 |  5.42e+00 +/- 1.4e-01  |  5.80e+00 +/- 8.8e-02  |
 test_objective_compile_dshape_current   |     +0.37 +/- 2.01     | +1.44e-02 +/- 7.90e-02 |  3.95e+00 +/- 6.0e-02  |  3.94e+00 +/- 5.1e-02  |
 test_objective_compute_dshape_current   |     +5.30 +/- 4.27     | +2.71e-04 +/- 2.19e-04 |  5.40e-03 +/- 2.1e-04  |  5.13e-03 +/- 5.9e-05  |
 test_objective_jac_dshape_current       |     +3.52 +/- 6.10     | +1.48e-03 +/- 2.57e-03 |  4.36e-02 +/- 1.1e-03  |  4.22e-02 +/- 2.3e-03  |
 test_perturb_2                          |     +2.77 +/- 2.14     | +5.49e-01 +/- 4.24e-01 |  2.03e+01 +/- 2.9e-01  |  1.98e+01 +/- 3.1e-01  |
 test_proximal_freeb_jac                 |     -0.34 +/- 2.24     | -2.54e-02 +/- 1.66e-01 |  7.40e+00 +/- 7.2e-02  |  7.42e+00 +/- 1.5e-01  |
 test_solve_fixed_iter                   |     +0.33 +/- 1.91     | +1.06e-01 +/- 6.23e-01 |  3.26e+01 +/- 4.3e-01  |  3.25e+01 +/- 4.5e-01  |
 test_LinearConstraintProjection_build   |     -0.48 +/- 3.87     | -5.24e-02 +/- 4.21e-01 |  1.08e+01 +/- 3.7e-01  |  1.09e+01 +/- 2.0e-01  |
 test_build_transform_fft_midres         |     -0.22 +/- 2.79     | -1.33e-03 +/- 1.70e-02 |  6.07e-01 +/- 1.4e-02  |  6.08e-01 +/- 9.0e-03  |
 test_build_transform_fft_highres        |     -1.20 +/- 1.24     | -1.17e-02 +/- 1.22e-02 |  9.67e-01 +/- 5.8e-03  |  9.78e-01 +/- 1.1e-02  |
 test_equilibrium_init_lowres            |     -0.38 +/- 1.63     | -1.48e-02 +/- 6.28e-02 |  3.84e+00 +/- 2.4e-02  |  3.85e+00 +/- 5.8e-02  |
 test_objective_compile_atf              |     +0.34 +/- 1.12     | +2.73e-02 +/- 9.07e-02 |  8.14e+00 +/- 7.1e-02  |  8.11e+00 +/- 5.6e-02  |
 test_objective_compute_atf              |     +3.50 +/- 4.28     | +5.55e-04 +/- 6.79e-04 |  1.64e-02 +/- 6.1e-04  |  1.59e-02 +/- 3.0e-04  |
 test_objective_jac_atf                  |     -2.26 +/- 2.47     | -4.49e-02 +/- 4.89e-02 |  1.94e+00 +/- 4.1e-02  |  1.98e+00 +/- 2.7e-02  |
 test_perturb_1                          |     -0.55 +/- 1.13     | -8.19e-02 +/- 1.67e-01 |  1.47e+01 +/- 1.4e-01  |  1.48e+01 +/- 9.3e-02  |
 test_proximal_jac_atf                   |     -0.12 +/- 1.26     | -1.00e-02 +/- 1.04e-01 |  8.24e+00 +/- 8.0e-02  |  8.25e+00 +/- 6.6e-02  |
 test_proximal_freeb_compute             |     -0.75 +/- 0.87     | -1.50e-03 +/- 1.75e-03 |  1.99e-01 +/- 1.1e-03  |  2.00e-01 +/- 1.4e-03  |
 test_solve_fixed_iter_compiled          |     +0.07 +/- 0.56     | +1.37e-02 +/- 1.15e-01 |  2.05e+01 +/- 9.9e-02  |  2.05e+01 +/- 5.9e-02  |

[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]

This should be either combined or ahead/behind #1342 as they modify the same notebook. I would be fine to just make those changes into this PR and close the other one tbh to avoid the notebook merge conflict headaches

[dpanici]

I don't understand why for this PR tests fails due to too large of a diff, but for #1342 the tests are able to run?

[dpanici]

I don't understand why for this PR tests fails due to too large of a diff, but for #1342 the tests are able to run?

This seems fixed now? weird

[dpanici]

Sorry, forgot I had not meant to merge in #1342 before this one. I can deal with the merge conflict if you want, I think using nbdime would make it easier so I can try that out

[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