ko/coils quad flux

[kianorr]

Adds quadratic flux objective function.

Resolves #901

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     -6.03 +/- 3.20     | -1.48e-03 +/- 7.86e-04 |  2.31e-02 +/- 4.4e-04  |  2.45e-02 +/- 6.5e-04  |
+test_build_transform_fft_midres         |     -4.28 +/- 0.93     | -5.92e-03 +/- 1.28e-03 |  1.32e-01 +/- 8.4e-04  |  1.38e-01 +/- 9.7e-04  |
+test_build_transform_fft_highres        |     -3.57 +/- 1.03     | -2.26e-02 +/- 6.54e-03 |  6.10e-01 +/- 3.4e-03  |  6.33e-01 +/- 5.6e-03  |
 test_equilibrium_init_lowres            |     -1.60 +/- 2.45     | -1.64e-02 +/- 2.53e-02 |  1.01e+00 +/- 1.6e-02  |  1.03e+00 +/- 1.9e-02  |
 test_equilibrium_init_medres            |     -2.65 +/- 2.12     | -4.08e-02 +/- 3.27e-02 |  1.50e+00 +/- 2.8e-02  |  1.54e+00 +/- 1.6e-02  |
 test_equilibrium_init_highres           |     -2.59 +/- 1.01     | -9.51e-02 +/- 3.72e-02 |  3.57e+00 +/- 2.7e-02  |  3.67e+00 +/- 2.6e-02  |
 test_objective_compile_dshape_current   |     -0.55 +/- 5.32     | -3.58e-02 +/- 3.48e-01 |  6.50e+00 +/- 1.9e-01  |  6.54e+00 +/- 2.9e-01  |
 test_objective_compile_atf              |     +9.19 +/- 5.32     | +1.72e+00 +/- 9.93e-01 |  2.04e+01 +/- 6.0e-01  |  1.87e+01 +/- 7.9e-01  |
 test_objective_compute_dshape_current   |     -6.75 +/- 4.34     | -2.93e-04 +/- 1.88e-04 |  4.04e-03 +/- 1.0e-04  |  4.33e-03 +/- 1.6e-04  |
 test_objective_compute_atf              |     +3.86 +/- 9.26     | +5.65e-04 +/- 1.36e-03 |  1.52e-02 +/- 1.2e-03  |  1.46e-02 +/- 6.8e-04  |
 test_objective_jac_dshape_current       |    +16.23 +/- 12.06    | +2.58e-02 +/- 1.91e-02 |  1.85e-01 +/- 1.8e-02  |  1.59e-01 +/- 7.0e-03  |
-test_objective_jac_atf                  |    +16.91 +/- 2.06     | +1.35e+00 +/- 1.65e-01 |  9.33e+00 +/- 1.4e-01  |  7.98e+00 +/- 7.8e-02  |
 test_perturb_1                          |    +35.04 +/- 14.51    | +3.77e+00 +/- 1.56e+00 |  1.45e+01 +/- 1.2e+00  |  1.08e+01 +/- 1.0e+00  |
-test_perturb_2                          |    +17.19 +/- 5.28     | +3.54e+00 +/- 1.09e+00 |  2.42e+01 +/- 6.0e-01  |  2.06e+01 +/- 9.1e-01  |

[YigitElma]

Review for APC524 homework, pull request review part.

[kianorr]

Not sure if having QuadraticFlux in _free_boundary.py is appropriate but I'm not sure where you all would prefer to put it

[dpanici]

• Add docstring to the compute function
• Add an eq_fixed option to this so that you can only optiimze an external field given a fixed equilibrium
• Add a test where you optimize a field with quadratic flux, something like this might work I think (since the equilibrum is axisymmetric the optimizer should put the non-axisymmetric part of the external field to zero, i.e. zero out the Phi_mn, though if this does not work lmk)

eq = Equilibrium(M=2,L=2)
eq.solve(verbose=0)
surf = eq.surface.copy()
surf.R_lmn[surf.R_basis.get_idx(M=1,N=0)] = 2
surf.Z_lmn[surf.Z_basis.get_idx(M=-1,N=0)] = 2

field = FourierCurrentPotentialField.from_surface(surface=surf, Phi_mn=np.array([1e4]),modes_Phi=np.array([[1,4]])),G=1e4)

constraints=(FixParameter(eq), # this line is unneeded when eq_fixed is implemented
                     FixParameter(field,["I","G","R_lmn","Z_lmn"]))
optimizer = Optimizer("lsq-exact")
obj = ObjectiveFunction(QuadraticFlux(ext_field=field,eq=eq))
(eq,field) = optimizer.optimize((eq,field),objective=obj,constraints=constraints,ftol=1e-15,xtol=1e-15)
np.testing.assert_allclose(field.Phi_mn,0,atol=1e-14)

[ddudt]

Since the QuadraticFlux objective assumes the Equilibrium is held fixed during the optimization, I think we need to add a check for that. Like if QuadraticFlux is in optimizer.objective, then we should throw an error if eq is in optimizer.things.

[ddudt]

Why use the initial equilibrium from this solve and not the "real" precise QA equilibrium?

[f0uriest]

Since the QuadraticFlux objective assumes the Equilibrium is held fixed during the optimization, I think we need to add a check for that. Like if QuadraticFlux is in optimizer.objective, then we should throw an error if eq is in optimizer.things.

This is a good idea, I'll add this.