Update equilibria in desc.examples

[f0uriest]

Resolves #1185
Resolves #1186

Re-ran them all and manually verified they look good by eye and the usual metrics (low force error etc).

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     +1.94 +/- 7.86     | +1.03e-02 +/- 4.16e-02 |  5.40e-01 +/- 3.6e-02  |  5.30e-01 +/- 2.2e-02  |
 test_equilibrium_init_medres            |     +0.45 +/- 2.10     | +1.89e-02 +/- 8.84e-02 |  4.22e+00 +/- 6.3e-02  |  4.20e+00 +/- 6.2e-02  |
 test_equilibrium_init_highres           |     -0.78 +/- 1.84     | -4.35e-02 +/- 1.03e-01 |  5.54e+00 +/- 7.2e-02  |  5.58e+00 +/- 7.4e-02  |
 test_objective_compile_dshape_current   |     -0.46 +/- 2.50     | -1.85e-02 +/- 9.98e-02 |  3.97e+00 +/- 7.0e-02  |  3.98e+00 +/- 7.2e-02  |
 test_objective_compute_dshape_current   |     -4.06 +/- 1.79     | -2.18e-04 +/- 9.60e-05 |  5.15e-03 +/- 6.7e-05  |  5.36e-03 +/- 6.9e-05  |
 test_objective_jac_dshape_current       |     +0.10 +/- 5.27     | +4.17e-05 +/- 2.29e-03 |  4.34e-02 +/- 2.0e-03  |  4.34e-02 +/- 1.1e-03  |
 test_perturb_2                          |     -1.05 +/- 2.86     | -2.10e-01 +/- 5.76e-01 |  1.99e+01 +/- 3.6e-01  |  2.01e+01 +/- 4.5e-01  |
 test_proximal_freeb_jac                 |     -0.03 +/- 1.26     | -2.21e-03 +/- 9.34e-02 |  7.44e+00 +/- 7.3e-02  |  7.44e+00 +/- 5.9e-02  |
-test_solve_fixed_iter                   |    +10.44 +/- 1.42     | +3.19e+00 +/- 4.34e-01 |  3.37e+01 +/- 3.2e-01  |  3.06e+01 +/- 2.9e-01  |
+test_LinearConstraintProjection_build   |    -55.72 +/- 1.72     | -1.35e+01 +/- 4.19e-01 |  1.08e+01 +/- 3.7e-01  |  2.43e+01 +/- 2.0e-01  |
+test_build_transform_fft_midres         |    -11.20 +/- 3.08     | -7.65e-02 +/- 2.10e-02 |  6.06e-01 +/- 1.4e-02  |  6.83e-01 +/- 1.6e-02  |
 test_build_transform_fft_highres        |     -6.84 +/- 4.62     | -7.19e-02 +/- 4.86e-02 |  9.79e-01 +/- 4.6e-02  |  1.05e+00 +/- 1.5e-02  |
 test_equilibrium_init_lowres            |    -10.86 +/- 8.74     | -4.93e-01 +/- 3.97e-01 |  4.05e+00 +/- 3.9e-01  |  4.54e+00 +/- 8.5e-02  |
 test_objective_compile_atf              |     +7.64 +/- 4.83     | +6.18e-01 +/- 3.91e-01 |  8.70e+00 +/- 2.8e-01  |  8.08e+00 +/- 2.7e-01  |
 test_objective_compute_atf              |     +0.59 +/- 3.51     | +9.30e-05 +/- 5.53e-04 |  1.58e-02 +/- 5.3e-04  |  1.57e-02 +/- 1.7e-04  |
 test_objective_jac_atf                  |     +4.34 +/- 7.65     | +8.62e-02 +/- 1.52e-01 |  2.07e+00 +/- 1.5e-01  |  1.99e+00 +/- 1.8e-02  |
 test_perturb_1                          |     +0.02 +/- 6.60     | +2.95e-03 +/- 9.71e-01 |  1.47e+01 +/- 5.1e-01  |  1.47e+01 +/- 8.3e-01  |
 test_proximal_jac_atf                   |     -0.75 +/- 1.09     | -6.25e-02 +/- 9.00e-02 |  8.23e+00 +/- 5.5e-02  |  8.30e+00 +/- 7.1e-02  |
 test_proximal_freeb_compute             |     -0.13 +/- 1.05     | -2.51e-04 +/- 2.11e-03 |  2.00e-01 +/- 1.5e-03  |  2.01e-01 +/- 1.4e-03  |
-test_solve_fixed_iter_compiled          |    +26.34 +/- 7.06     | +4.61e+00 +/- 1.24e+00 |  2.21e+01 +/- 1.1e+00  |  1.75e+01 +/- 4.7e-01  |

[dpanici]

This might change/need checking again once #1073 is in (or maybe base this off of #1073?)

[dpanici]

I will approve this once merge conflict is resolved, but I also want to note that I'd like each notebook to be re-ran as well. The 3D plot-containing ones may have to be each separate PRs to avoid the issues we have with the git diffs being too large and failing our tests. I will make an issue for this

[dpanici]

Could try to reduce test time as well #914 by reducing res or not doing continuation for some of the examples

[dpanici]

what is this doing? seems to be passing in the same modes for Rn as Zn?

[dpanici]

That seems off? or do we ensure before this that we have the full mode spectrum in n and just set the non-symmetric modes to zero if it is stell symmetric?

[YigitElma]

I think we can also reduce the radial resolution of ATF and HELITRON (also change some solver tolerances) to get the same equilibrium, as you did here for W7-X. Those are the simplest examples but have the highest radial resolution. It would help reducing the CI testing time too.

[YigitElma]

I found these to be also working. For ATF,

# spectral resolution
L_rad  =  8, 16
M_pol  =  12
N_tor  =  0x4, 4
M_grid =  12, 16
N_grid =  0x4, 6

For HELIOTRON,

# spectral resolution
L_rad  =  8, 18
M_pol  =  6, 12
N_tor  =  0,  0,  3
M_grid =  12, 18
N_grid =  0,  0,  6

[f0uriest]

I found these to be also working. For ATF,

# spectral resolution
L_rad  =  8, 16
M_pol  =  12
N_tor  =  0x4, 4
M_grid =  12, 16
N_grid =  0x4, 6

For HELIOTRON,

# spectral resolution
L_rad  =  8, 18
M_pol  =  6, 12
N_tor  =  0,  0,  3
M_grid =  12, 18
N_grid =  0,  0,  6

Reducing the resolution causes some tests to fail so I'm keeping the old one for now. You can make a new PR for those if you want.

[YigitElma]

I found these to be also working. For ATF,

# spectral resolution
L_rad  =  8, 16
M_pol  =  12
N_tor  =  0x4, 4
M_grid =  12, 16
N_grid =  0x4, 6

For HELIOTRON,

# spectral resolution
L_rad  =  8, 18
M_pol  =  6, 12
N_tor  =  0,  0,  3
M_grid =  12, 18
N_grid =  0,  0,  6

Reducing the resolution causes some tests to fail so I'm keeping the old one for now. You can make a new PR for those if you want.

Thanks for trying🙏