Stop modding of non-periodic angles

[unalmis]

Resolves #1180 and resolves #1173 .

Here is what $\theta$ looks like now on #1119 :

Likewise, all the other quantities have become smooth bumps, as desired.

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     -3.13 +/- 7.15     | -1.71e-02 +/- 3.90e-02 |  5.28e-01 +/- 3.3e-02  |  5.45e-01 +/- 2.1e-02  |
 test_equilibrium_init_medres            |     -1.40 +/- 2.64     | -5.92e-02 +/- 1.11e-01 |  4.16e+00 +/- 6.1e-02  |  4.22e+00 +/- 9.3e-02  |
 test_equilibrium_init_highres           |     -0.43 +/- 2.38     | -2.39e-02 +/- 1.32e-01 |  5.52e+00 +/- 7.9e-02  |  5.54e+00 +/- 1.1e-01  |
 test_objective_compile_dshape_current   |     -0.92 +/- 1.60     | -3.65e-02 +/- 6.36e-02 |  3.93e+00 +/- 5.4e-02  |  3.97e+00 +/- 3.4e-02  |
 test_objective_compute_dshape_current   |     +4.60 +/- 53.00    | +1.67e-04 +/- 1.93e-03 |  3.81e-03 +/- 1.9e-03  |  3.64e-03 +/- 3.3e-05  |
 test_objective_jac_dshape_current       |     -5.04 +/- 5.40     | -2.11e-03 +/- 2.26e-03 |  3.97e-02 +/- 1.4e-03  |  4.18e-02 +/- 1.8e-03  |
 test_perturb_2                          |     -1.12 +/- 3.03     | -2.00e-01 +/- 5.41e-01 |  1.76e+01 +/- 2.7e-01  |  1.78e+01 +/- 4.7e-01  |
 test_proximal_freeb_jac                 |     +0.33 +/- 4.39     | +2.49e-02 +/- 3.29e-01 |  7.52e+00 +/- 5.6e-02  |  7.50e+00 +/- 3.2e-01  |
 test_solve_fixed_iter                   |     -0.24 +/- 58.96    | -1.20e-02 +/- 2.97e+00 |  5.02e+00 +/- 2.1e+00  |  5.03e+00 +/- 2.1e+00  |
 test_build_transform_fft_midres         |     -0.21 +/- 6.68     | -1.29e-03 +/- 4.11e-02 |  6.14e-01 +/- 3.9e-02  |  6.16e-01 +/- 1.3e-02  |
 test_build_transform_fft_highres        |     -0.20 +/- 3.22     | -2.00e-03 +/- 3.24e-02 |  1.01e+00 +/- 3.1e-02  |  1.01e+00 +/- 1.1e-02  |
 test_equilibrium_init_lowres            |     -0.79 +/- 1.55     | -3.04e-02 +/- 5.97e-02 |  3.82e+00 +/- 4.2e-02  |  3.85e+00 +/- 4.3e-02  |
 test_objective_compile_atf              |     +0.35 +/- 1.17     | +2.79e-02 +/- 9.36e-02 |  8.01e+00 +/- 6.3e-02  |  7.98e+00 +/- 6.9e-02  |
 test_objective_compute_atf              |     -0.93 +/- 2.07     | -9.81e-05 +/- 2.18e-04 |  1.04e-02 +/- 1.9e-04  |  1.05e-02 +/- 1.0e-04  |
 test_objective_jac_atf                  |     -0.63 +/- 3.29     | -1.23e-02 +/- 6.43e-02 |  1.94e+00 +/- 3.5e-02  |  1.96e+00 +/- 5.4e-02  |
 test_perturb_1                          |     +0.19 +/- 2.04     | +2.39e-02 +/- 2.53e-01 |  1.25e+01 +/- 1.7e-01  |  1.24e+01 +/- 1.8e-01  |
 test_proximal_jac_atf                   |     -0.17 +/- 1.02     | -1.41e-02 +/- 8.34e-02 |  8.16e+00 +/- 5.6e-02  |  8.18e+00 +/- 6.2e-02  |
 test_proximal_freeb_compute             |     +0.15 +/- 1.34     | +2.77e-04 +/- 2.48e-03 |  1.85e-01 +/- 1.3e-03  |  1.85e-01 +/- 2.1e-03  |

[codecov]

Codecov Report

Attention: Patch coverage is 96.42857% with 1 line in your changes missing coverage. Please review.

Project coverage is 95.45%. Comparing base (54becdb) to head (97d1747).
Report is 2175 commits behind head on master.

Files with missing lines	Patch %	Lines
desc/equilibrium/coords.py	95.45%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1254      +/-   ##
==========================================
- Coverage   95.45%   95.45%   -0.01%     
==========================================
  Files          95       95              
  Lines       23429    23423       -6     
==========================================
- Hits        22364    22358       -6     
  Misses       1065     1065              

Files with missing lines	Coverage Δ
desc/compute/_core.py	100.00% <100.00%> (ø)
desc/equilibrium/equilibrium.py	95.71% <ø> (ø)
desc/grid.py	93.07% <ø> (ø)
desc/vmec.py	91.91% <100.00%> (+<0.01%)	⬆️
desc/equilibrium/coords.py	88.42% <95.45%> (-0.33%)	⬇️

... and 2 files with indirect coverage changes

[rahulgaur104]

Here is what θ looks like now on #1119

Does it work for negative zeta values? What if I give zeta in [-4pi, 4pi] to map_coordinates. Will the theta still be smooth?

[unalmis]

Here is what θ looks like now on #1119

Does it work for negative zeta values? What if I give zeta in [-4pi, 4pi] to map_coordinates. Will the theta still be smooth?

Where we start $\zeta$ seems to not matter. However there is still an issue, I believe completely separate to this PR. I have found that $\theta$ is still discontinuous every two toroidal transits, which is causing issues: #1119 (comment).

Here is a plot of $\theta(\alpha=0, \zeta)$.

maybe something with $\lambda$?

[rahulgaur104]

Approving, but I am slightly concerned that it might break the ballooning PR.
Merge at will.

[unalmis]

For the equilibrium I computed this plot on, two toroidal transits corresponds to one poloidal transit. So it seems the information of which poloidal transit $\theta$ is at is lost somewhere

[unalmis]

So the issue is probably that I'm paramterizing my FourierChebyshev series for $\theta$ using $\alpha \in [-\pi, \pi]$ and I should be using $\alpha \in [0, 2 \pi]$. I'll look into this on the weekend.

[unalmis]

I resolved the remaining discontinuous issue fyi.