change field line integration to use diffrax

[dpanici]

Updated comment by @f0uriest

• field_line_integrate now uses diffrax instead of jax.experimental.ode.odeint which has been soft deprecated.
• Allows better control of bounding box (hard stop of field lines rather than ad-hoc expoential decay)
• In practice seems to be a bit faster. test_plot_poincare which calls field_line_integrate under the hood went from ~65s to ~55s with these changes.

Resolves #609

[dpanici]

The RuntimeWarning for numpy header size being different is still an issue, I think because the warning is coming from C level code (@f0uriest @unalmis any ideas on how to ignore those? seems like a filterwarnings problem), right now I have in a blanket ignore RuntimeWarning but that is not really what we want, I opened an issue to see if pytest knows how to resolve it pytest-dev/pytest#11304

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.45%. Comparing base (a4220a4) to head (acf1c98).
Report is 2206 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #610      +/-   ##
==========================================
- Coverage   95.45%   95.45%   -0.01%     
==========================================
  Files          95       95              
  Lines       23419    23429      +10     
==========================================
+ Hits        22354    22363       +9     
- Misses       1065     1066       +1     

Files with missing lines	Coverage Δ
desc/magnetic_fields/_core.py	96.61% <100.00%> (+0.04%)	⬆️

... and 2 files with indirect coverage changes

[f0uriest]

it looks like there are older versions of diffrax that work with older versions of jax. They might not have the discrete terminating event stuff but might still be useful for being able to select different integration schemes etc.

[dpanici]

exp. decrease RHS outside the bounding box (exp(-r)*B)
and try older version

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_midres         |     -3.98 +/- 5.49     | -2.57e-02 +/- 3.55e-02 |  6.21e-01 +/- 3.1e-02  |  6.46e-01 +/- 1.7e-02  |
 test_build_transform_fft_highres        |     -5.12 +/- 3.82     | -5.40e-02 +/- 4.03e-02 |  1.00e+00 +/- 3.8e-02  |  1.06e+00 +/- 1.4e-02  |
 test_equilibrium_init_lowres            |     -6.77 +/- 2.85     | -2.81e-01 +/- 1.19e-01 |  3.87e+00 +/- 8.7e-02  |  4.15e+00 +/- 8.0e-02  |
 test_objective_compile_atf              |     -0.44 +/- 3.12     | -3.49e-02 +/- 2.48e-01 |  7.93e+00 +/- 2.1e-01  |  7.96e+00 +/- 1.3e-01  |
 test_objective_compute_atf              |     -0.53 +/- 2.12     | -5.40e-05 +/- 2.17e-04 |  1.02e-02 +/- 1.1e-04  |  1.02e-02 +/- 1.9e-04  |
 test_objective_jac_atf                  |     +0.26 +/- 1.38     | +4.96e-03 +/- 2.65e-02 |  1.92e+00 +/- 1.7e-02  |  1.92e+00 +/- 2.1e-02  |
 test_perturb_1                          |     +2.56 +/- 5.52     | +3.16e-01 +/- 6.80e-01 |  1.26e+01 +/- 5.8e-01  |  1.23e+01 +/- 3.5e-01  |
 test_proximal_jac_atf                   |     +0.34 +/- 1.47     | +2.78e-02 +/- 1.19e-01 |  8.12e+00 +/- 6.9e-02  |  8.09e+00 +/- 9.7e-02  |
 test_proximal_freeb_compute             |     +2.33 +/- 1.08     | +4.26e-03 +/- 1.98e-03 |  1.87e-01 +/- 1.5e-03  |  1.83e-01 +/- 1.2e-03  |
 test_build_transform_fft_lowres         |     +0.30 +/- 6.13     | +1.60e-03 +/- 3.26e-02 |  5.33e-01 +/- 2.4e-02  |  5.31e-01 +/- 2.1e-02  |
 test_equilibrium_init_medres            |     +1.40 +/- 5.57     | +5.74e-02 +/- 2.29e-01 |  4.17e+00 +/- 2.3e-01  |  4.11e+00 +/- 3.5e-02  |
 test_equilibrium_init_highres           |     +1.59 +/- 2.35     | +8.64e-02 +/- 1.28e-01 |  5.53e+00 +/- 1.2e-01  |  5.45e+00 +/- 4.5e-02  |
 test_objective_compile_dshape_current   |     +0.40 +/- 1.18     | +1.54e-02 +/- 4.49e-02 |  3.82e+00 +/- 8.8e-03  |  3.81e+00 +/- 4.4e-02  |
 test_objective_compute_dshape_current   |     +0.63 +/- 1.60     | +2.19e-05 +/- 5.52e-05 |  3.48e-03 +/- 3.9e-05  |  3.46e-03 +/- 3.9e-05  |
 test_objective_jac_dshape_current       |     -1.70 +/- 5.33     | -6.86e-04 +/- 2.14e-03 |  3.96e-02 +/- 1.4e-03  |  4.03e-02 +/- 1.6e-03  |
 test_perturb_2                          |     +0.48 +/- 1.96     | +8.30e-02 +/- 3.38e-01 |  1.73e+01 +/- 1.9e-01  |  1.72e+01 +/- 2.8e-01  |
 test_proximal_freeb_jac                 |     -0.42 +/- 0.77     | -3.18e-02 +/- 5.76e-02 |  7.48e+00 +/- 3.2e-02  |  7.51e+00 +/- 4.8e-02  |
 test_solve_fixed_iter                   |     -0.31 +/- 61.51    | -1.52e-02 +/- 3.05e+00 |  4.95e+00 +/- 2.2e+00  |  4.96e+00 +/- 2.1e+00  |

[f0uriest]

@dpanici I know you can't formally approve this but lmk if you have any comments

[YigitElma]

why do we use another integrator for this test (an implicit one?)? Maybe we should specify some integrator options for the user to choose depending on the case. Or basically reference https://docs.kidger.site/diffrax/api/solvers/ode_solvers/

[f0uriest]

Dopri5 and Tsit5 are both rk45 methods, just with slightly different coefficients. There's not any real reason to prefer one over the other, other than to just test that they both work.

[YigitElma]

Suggested change

	).squeeze()
	# step along the field line
	# Torodial component of the field is used to normalize the step size
	return jnp.array(
	jnp.sign(bp) * [r * br / bp, 1, r * bz / bp]
	).squeeze()

[YigitElma]

Not that important if you don't change

[f0uriest]

it's not that we're normalizing the step or anything, its just because we're using the toroidal angle as our "time" coordinate so that modifies the ODE slightly.