add basic coil objectives

[kianorr]

Adds coil length objective

Resolves #895
Resolves #897
Resolves #896
Resolves #863

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     +8.77 +/- 4.22     | +1.58e-01 +/- 7.58e-02 |  1.95e+00 +/- 6.4e-02  |  1.80e+00 +/- 4.0e-02  |
 test_build_transform_fft_midres         |     +2.93 +/- 4.46     | +6.01e-02 +/- 9.16e-02 |  2.11e+00 +/- 5.6e-02  |  2.05e+00 +/- 7.2e-02  |
 test_build_transform_fft_highres        |     +3.48 +/- 3.96     | +8.39e-02 +/- 9.55e-02 |  2.50e+00 +/- 7.7e-02  |  2.41e+00 +/- 5.6e-02  |
 test_equilibrium_init_lowres            |     +2.09 +/- 5.13     | +2.15e-01 +/- 5.27e-01 |  1.05e+01 +/- 3.9e-01  |  1.03e+01 +/- 3.5e-01  |
 test_equilibrium_init_medres            |     +2.73 +/- 3.06     | +2.98e-01 +/- 3.35e-01 |  1.12e+01 +/- 2.5e-01  |  1.09e+01 +/- 2.3e-01  |
 test_equilibrium_init_highres           |     +3.98 +/- 3.35     | +4.96e-01 +/- 4.17e-01 |  1.29e+01 +/- 3.4e-01  |  1.25e+01 +/- 2.5e-01  |
 test_objective_compile_dshape_current   |     -0.94 +/- 1.71     | -3.82e-02 +/- 6.92e-02 |  4.01e+00 +/- 5.4e-02  |  4.05e+00 +/- 4.3e-02  |
 test_objective_compile_atf              |     +0.20 +/- 5.47     | +1.52e-02 +/- 4.17e-01 |  7.64e+00 +/- 3.4e-01  |  7.63e+00 +/- 2.5e-01  |
 test_objective_compute_dshape_current   |     +0.42 +/- 7.64     | +1.90e-05 +/- 3.48e-04 |  4.58e-03 +/- 3.3e-04  |  4.56e-03 +/- 1.1e-04  |
 test_objective_compute_atf              |     +2.59 +/- 3.98     | +4.71e-04 +/- 7.24e-04 |  1.87e-02 +/- 6.6e-04  |  1.82e-02 +/- 2.9e-04  |
 test_objective_jac_dshape_current       |     -2.07 +/- 7.25     | -8.75e-04 +/- 3.06e-03 |  4.13e-02 +/- 2.4e-03  |  4.22e-02 +/- 1.9e-03  |
 test_objective_jac_atf                  |     +1.54 +/- 3.16     | +2.84e-02 +/- 5.83e-02 |  1.87e+00 +/- 4.6e-02  |  1.84e+00 +/- 3.6e-02  |
 test_perturb_1                          |     +0.97 +/- 3.79     | +1.51e-01 +/- 5.86e-01 |  1.56e+01 +/- 4.9e-01  |  1.55e+01 +/- 3.2e-01  |
 test_perturb_2                          |     +2.06 +/- 1.67     | +4.23e-01 +/- 3.43e-01 |  2.10e+01 +/- 3.1e-01  |  2.05e+01 +/- 1.5e-01  |
 test_proximal_jac_atf                   |     +0.52 +/- 1.68     | +3.74e-02 +/- 1.21e-01 |  7.21e+00 +/- 1.0e-01  |  7.17e+00 +/- 6.4e-02  |
 test_proximal_freeb_compute             |     -0.08 +/- 1.09     | -9.54e-05 +/- 1.30e-03 |  1.20e-01 +/- 7.8e-04  |  1.20e-01 +/- 1.0e-03  |
 test_proximal_freeb_jac                 |     -2.01 +/- 2.36     | -1.49e-01 +/- 1.74e-01 |  7.23e+00 +/- 7.6e-02  |  7.38e+00 +/- 1.6e-01  |

[codecov]

Codecov Report

Attention: Patch coverage is 97.81022% with 3 lines in your changes are missing coverage. Please review.

Project coverage is 94.64%. Comparing base (a1181fb) to head (b0662cc).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #853      +/-   ##
==========================================
+ Coverage   94.62%   94.64%   +0.01%     
==========================================
  Files          86       87       +1     
  Lines       21606    21740     +134     
==========================================
+ Hits        20444    20575     +131     
- Misses       1162     1165       +3     

Files	Coverage Δ
desc/backend.py	89.67% <100.00%> (ø)
desc/coils.py	98.50% <100.00%> (ø)
desc/objectives/__init__.py	100.00% <100.00%> (ø)
desc/objectives/normalization.py	96.55% <100.00%> (+0.18%)	⬆️
desc/objectives/_coils.py	97.69% <97.69%> (ø)

[dpanici]

Merge #840 and see if it works

[kianorr]

Merge #840 and see if it works

I merged #840 in and the test that I have is passing now.

[dpanici]

Might want to merge again, idt any tests should fail from the compute function side

[f0uriest]

Should get another review from @dpanici before merging

[ddudt]

Should get another review from @dpanici before merging

I would like to look at it too, if you don't mind waiting a day

[kianorr]

I would like to look at it too, if you don't mind waiting a day

Of course, go for it but I'd like to merge it sooner rather than later

[dpanici]

change the docstring to address Rory's previous comment on loss functions

[kianorr]

change the docstring to address Rory's previous comment on loss functions

my bad, forgot to change it for all of them. thanks

[dpanici]

Instead of "Affects" can you say "operates over all coils, not each individial coil"? to make it more clear that it will make the error a scalar value, not a single value per coil

[ddudt]

If we are targeting a constant curvature value everywhere and only allowing a single Fourier mode, can we also check that the Fourier coefficient is the value we expect after the optimization? And/or allow more Fourier modes in the optimization and check that those higher order modes are close to zero?

[f0uriest]

FourierRZCurve is non-planar, so there are multiple shapes that have constant curvature, so I don't think there is an "expected" value for any of the coefficients.

[ddudt]

The coil is guaranteed to be planar since we are only allowing it to have a single Fourier mode. And in this test coil.Z_n stays exactly at 0 and coil.R_n changes from [10, 0] to approximately [9, 0] (see picture: blue is the original coil, red is optimized)