TwoPowerProfile

[ddudt]

New class for profiles of the form $f(\rho) = a(1-\rho^b)^c$ where $a$, $b$, $c$ are all floats. This is equivalent to the "two_power" profile input format in VMEC.

[codecov]

Codecov Report

Attention: Patch coverage is 94.59459% with 2 lines in your changes are missing coverage. Please review.

Project coverage is 95.34%. Comparing base (d9acdfa) to head (bb6cae0).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #984      +/-   ##
==========================================
- Coverage   95.34%   95.34%   -0.01%     
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  Files          87       87              
  Lines       21890    21926      +36     
==========================================
+ Hits        20871    20905      +34     
- Misses       1019     1021       +2     

Files	Coverage Δ
desc/profiles.py	97.21% <94.59%> (-0.20%)	⬇️

[f0uriest]

isnt this only true if b,c are floats <dr?

what is the use case for b,c being floats rather than ints?

my worry is also that if b<1 than the derivative blows up at r=0 as well.

[ddudt]

True, depending on the parameter values it may or may not blow up at $\rho=0$ and/or $\rho=1$.

My personal use case is to use an integer b = 1 or 2, and c as a float. But if these numbers are optimizable params they all need to be floats.

Options:

1. Add a check to make sure b >= 1. But there isn't much we can do about c.
2. We don't need to merge this into the master branch. But I coded it up anyways so I figured I would share it.

[f0uriest]

My question is, do they all need to be optimizable? We could just make b,c constant integers and leave a optimizable?

Along a similar vein, VMEC has a bunch of other profiles types that might be worth looking at: https://github.com/jonathanschilling/educational_VMEC/blob/master/src/profile_functions.f

I have some VMEC input files that use the atan and two-lorentz profiles that would be good to try in DESC.

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     -2.47 +/- 3.51     | -4.60e-02 +/- 6.54e-02 |  1.82e+00 +/- 5.0e-02  |  1.86e+00 +/- 4.2e-02  |
 test_build_transform_fft_midres         |     -3.03 +/- 4.08     | -6.25e-02 +/- 8.43e-02 |  2.00e+00 +/- 5.3e-02  |  2.07e+00 +/- 6.6e-02  |
 test_build_transform_fft_highres        |     -1.94 +/- 3.25     | -4.77e-02 +/- 8.00e-02 |  2.41e+00 +/- 5.8e-02  |  2.46e+00 +/- 5.5e-02  |
 test_equilibrium_init_lowres            |     -2.03 +/- 3.93     | -2.05e-01 +/- 3.96e-01 |  9.87e+00 +/- 1.7e-01  |  1.01e+01 +/- 3.6e-01  |
 test_equilibrium_init_medres            |     -3.47 +/- 2.25     | -3.68e-01 +/- 2.38e-01 |  1.02e+01 +/- 1.6e-01  |  1.06e+01 +/- 1.8e-01  |
 test_equilibrium_init_highres           |     -1.68 +/- 2.16     | -2.09e-01 +/- 2.69e-01 |  1.22e+01 +/- 2.1e-01  |  1.24e+01 +/- 1.7e-01  |
 test_objective_compile_dshape_current   |     -2.13 +/- 10.49    | -7.84e-02 +/- 3.87e-01 |  3.61e+00 +/- 2.5e-01  |  3.69e+00 +/- 3.0e-01  |
 test_objective_compile_atf              |     -1.18 +/- 2.75     | -8.75e-02 +/- 2.04e-01 |  7.32e+00 +/- 1.6e-01  |  7.40e+00 +/- 1.3e-01  |
 test_objective_compute_dshape_current   |     -4.26 +/- 5.02     | -1.75e-04 +/- 2.06e-04 |  3.93e-03 +/- 7.7e-05  |  4.10e-03 +/- 1.9e-04  |
 test_objective_compute_atf              |     -0.20 +/- 7.27     | -3.65e-05 +/- 1.31e-03 |  1.80e-02 +/- 8.4e-04  |  1.80e-02 +/- 1.0e-03  |
 test_objective_jac_dshape_current       |     +0.24 +/- 9.42     | +1.03e-04 +/- 4.00e-03 |  4.26e-02 +/- 2.8e-03  |  4.25e-02 +/- 2.9e-03  |
 test_objective_jac_atf                  |     +0.27 +/- 3.52     | +5.09e-03 +/- 6.68e-02 |  1.91e+00 +/- 3.7e-02  |  1.90e+00 +/- 5.6e-02  |
 test_perturb_1                          |     +1.46 +/- 3.31     | +2.18e-01 +/- 4.96e-01 |  1.52e+01 +/- 2.3e-01  |  1.50e+01 +/- 4.4e-01  |
 test_perturb_2                          |     +1.52 +/- 4.56     | +3.04e-01 +/- 9.08e-01 |  2.02e+01 +/- 8.2e-01  |  1.99e+01 +/- 3.9e-01  |
 test_proximal_jac_atf                   |     +0.98 +/- 1.53     | +6.97e-02 +/- 1.10e-01 |  7.21e+00 +/- 9.6e-02  |  7.14e+00 +/- 5.2e-02  |
 test_proximal_freeb_compute             |     +1.98 +/- 0.82     | +2.52e-03 +/- 1.04e-03 |  1.30e-01 +/- 6.0e-04  |  1.28e-01 +/- 8.5e-04  |
 test_proximal_freeb_jac                 |     +0.32 +/- 1.61     | +2.33e-02 +/- 1.18e-01 |  7.37e+00 +/- 7.4e-02  |  7.35e+00 +/- 9.3e-02  |

[dpanici]

is it even physical then if b < 1?

[dpanici]

• add higher derivs
• add to docstring that the params are only good for certain parameter ranges
• add warning in build to warn if the parameters make things be divergent or nonphysical
• check if it overlaps with a VMEC one and if so, then we can say it is similar to that

[ddudt]

• add higher derivs
• add to docstring that the params are only good for certain parameter ranges
• add warning in build to warn if the parameters make things be divergent or nonphysical
• check if it overlaps with a VMEC one and if so, then we can say it is similar to that

• It turns out this is the same as the "two_power" profiles in VMEC, so I changed the name accordingly.
• The MTanhProfile is also only implemented up to derivative order dr=2. Do we actually need higher order derivatives?
• I added documentation and warnings for bad parameter values at initialization.

made requested changes

[dpanici]

see comments