CoilIntegratedCurvature objective

[ddudt]

A scalar version of convexity for a curve: $\int \kappa |\partial_s \mathbf{x}| ds = 2 \pi$

Similar to our existing CoilCurvature objective, which is signed to indicate convexity.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.69%. Comparing base (b3b6dcc) to head (e6b117c).
Report is 18 commits behind head on master.

Additional details and impacted files

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- Coverage   95.69%   95.69%   -0.01%     
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  Files         101      101              
  Lines       25614    25633      +19     
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+ Hits        24511    24529      +18     
- Misses       1103     1104       +1     

Files with missing lines	Coverage Δ
desc/objectives/__init__.py	100.00% <ø> (ø)
desc/objectives/_coils.py	99.36% <100.00%> (+0.01%)	⬆️

... and 1 file with indirect coverage changes

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     +6.35 +/- 4.95     | +3.65e-02 +/- 2.85e-02 |  6.12e-01 +/- 1.4e-02  |  5.76e-01 +/- 2.5e-02  |
-test_equilibrium_init_medres            |     +7.13 +/- 2.36     | +3.27e-01 +/- 1.08e-01 |  4.92e+00 +/- 4.2e-02  |  4.59e+00 +/- 9.9e-02  |
 test_equilibrium_init_highres           |     +4.40 +/- 2.45     | +2.63e-01 +/- 1.46e-01 |  6.23e+00 +/- 1.0e-01  |  5.97e+00 +/- 1.1e-01  |
 test_objective_compile_dshape_current   |     +2.09 +/- 5.37     | +9.53e-02 +/- 2.45e-01 |  4.66e+00 +/- 2.0e-01  |  4.56e+00 +/- 1.4e-01  |
 test_objective_compute_dshape_current   |     +6.79 +/- 14.27    | +3.71e-04 +/- 7.81e-04 |  5.84e-03 +/- 3.3e-04  |  5.47e-03 +/- 7.1e-04  |
 test_objective_jac_dshape_current       |     +0.48 +/- 10.08    | +2.26e-04 +/- 4.73e-03 |  4.71e-02 +/- 3.4e-03  |  4.69e-02 +/- 3.3e-03  |
 test_perturb_2                          |     +3.35 +/- 3.85     | +7.28e-01 +/- 8.37e-01 |  2.25e+01 +/- 2.1e-01  |  2.18e+01 +/- 8.1e-01  |
-test_proximal_freeb_jac                 |    +14.89 +/- 3.28     | +1.13e+00 +/- 2.48e-01 |  8.68e+00 +/- 1.3e-01  |  7.56e+00 +/- 2.1e-01  |
 test_solve_fixed_iter                   |     +5.38 +/- 4.14     | +1.82e+00 +/- 1.40e+00 |  3.57e+01 +/- 1.3e+00  |  3.39e+01 +/- 4.8e-01  |
 test_LinearConstraintProjection_build   |     -0.32 +/- 4.79     | -3.59e-02 +/- 5.33e-01 |  1.11e+01 +/- 3.9e-01  |  1.11e+01 +/- 3.7e-01  |
 test_build_transform_fft_midres         |     +0.82 +/- 3.30     | +5.05e-03 +/- 2.04e-02 |  6.25e-01 +/- 1.8e-02  |  6.20e-01 +/- 9.1e-03  |
 test_build_transform_fft_highres        |     +0.53 +/- 6.73     | +5.24e-03 +/- 6.65e-02 |  9.94e-01 +/- 6.4e-02  |  9.88e-01 +/- 1.9e-02  |
 test_equilibrium_init_lowres            |     -0.21 +/- 2.50     | -8.51e-03 +/- 9.97e-02 |  3.98e+00 +/- 6.9e-02  |  3.99e+00 +/- 7.2e-02  |
 test_objective_compile_atf              |     -0.54 +/- 1.74     | -4.53e-02 +/- 1.47e-01 |  8.37e+00 +/- 7.6e-02  |  8.42e+00 +/- 1.3e-01  |
 test_objective_compute_atf              |     +1.15 +/- 3.31     | +1.83e-04 +/- 5.29e-04 |  1.62e-02 +/- 4.0e-04  |  1.60e-02 +/- 3.4e-04  |
 test_objective_jac_atf                  |     -0.66 +/- 1.86     | -1.27e-02 +/- 3.59e-02 |  1.92e+00 +/- 2.4e-02  |  1.93e+00 +/- 2.6e-02  |
 test_perturb_1                          |     -0.35 +/- 2.32     | -5.26e-02 +/- 3.49e-01 |  1.50e+01 +/- 2.5e-01  |  1.50e+01 +/- 2.4e-01  |
 test_proximal_jac_atf                   |     +0.62 +/- 0.59     | +5.14e-02 +/- 4.85e-02 |  8.31e+00 +/- 4.2e-02  |  8.26e+00 +/- 2.4e-02  |
 test_proximal_freeb_compute             |     -0.50 +/- 1.56     | -1.02e-03 +/- 3.16e-03 |  2.02e-01 +/- 2.1e-03  |  2.03e-01 +/- 2.4e-03  |
 test_solve_fixed_iter_compiled          |     -0.60 +/- 0.94     | -1.26e-01 +/- 1.95e-01 |  2.07e+01 +/- 1.6e-01  |  2.08e+01 +/- 1.2e-01  |

[dpanici]

• give a self._endpoint attribute to CoilConvexity to be True
• check for this attribute in _CoilObjective.build to decide if endpoint should be true or not (False by default if hasattr(self._endpoint) is False
• move errorif statement to after super.build() in build of CoilConvexity
• make docstring clearer for CoilConvexity
• Fix docs

[dpanici]

Call it IntegratedCurvature

[f0uriest]

I think you can get the same thing if you leave off the endpoint and do (curvature*x_s*ds).sum(). The integrand is periodic so the endpoint and start are the same.

[ddudt]

This is slightly less accurate then the trapezoid integration (atol=2e-5 vs atol=1e-6 at the grid resolution used in the tests) but I still like this change for the simplicity.

made requested changes