ReduceQuadratureGrid number of radial points to match intended functionality

[dpanici]

• internally to QuadratureGrid, reduces the number of radial points fro L+1 to (L+2)//2, which is the minimum amount of points to integrate a polynomial of radial degree L with jacobi weight function exactly in general

Resolves #983

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     -4.22 +/- 11.80    | -2.14e-02 +/- 5.99e-02 |  4.86e-01 +/- 6.0e-02  |  5.08e-01 +/- 6.2e-03  |
 test_build_transform_fft_midres         |     -4.79 +/- 2.76     | -2.82e-02 +/- 1.63e-02 |  5.61e-01 +/- 1.5e-02  |  5.89e-01 +/- 5.3e-03  |
+test_build_transform_fft_highres        |     -5.84 +/- 1.58     | -5.75e-02 +/- 1.55e-02 |  9.28e-01 +/- 1.3e-02  |  9.85e-01 +/- 8.0e-03  |
 test_equilibrium_init_lowres            |     -2.90 +/- 3.91     | -1.05e-01 +/- 1.42e-01 |  3.52e+00 +/- 4.2e-02  |  3.62e+00 +/- 1.4e-01  |
 test_equilibrium_init_medres            |     -7.30 +/- 2.81     | -3.02e-01 +/- 1.16e-01 |  3.83e+00 +/- 7.3e-02  |  4.13e+00 +/- 9.0e-02  |
+test_equilibrium_init_highres           |     -9.04 +/- 2.11     | -5.06e-01 +/- 1.18e-01 |  5.10e+00 +/- 5.6e-02  |  5.60e+00 +/- 1.0e-01  |
+test_objective_compile_dshape_current   |     -6.56 +/- 2.02     | -2.53e-01 +/- 7.79e-02 |  3.61e+00 +/- 6.6e-02  |  3.86e+00 +/- 4.2e-02  |
 test_objective_compile_atf              |     -6.19 +/- 2.61     | -4.87e-01 +/- 2.05e-01 |  7.38e+00 +/- 6.3e-02  |  7.87e+00 +/- 2.0e-01  |
 test_objective_compute_dshape_current   |     -5.57 +/- 7.51     | -1.92e-04 +/- 2.59e-04 |  3.26e-03 +/- 2.6e-04  |  3.45e-03 +/- 2.6e-05  |
 test_objective_compute_atf              |     -2.25 +/- 5.46     | -2.32e-04 +/- 5.63e-04 |  1.01e-02 +/- 5.5e-04  |  1.03e-02 +/- 1.4e-04  |
 test_objective_jac_dshape_current       |     -0.23 +/- 8.01     | -8.99e-05 +/- 3.07e-03 |  3.82e-02 +/- 2.4e-03  |  3.83e-02 +/- 2.0e-03  |
 test_objective_jac_atf                  |     -5.01 +/- 4.92     | -9.61e-02 +/- 9.43e-02 |  1.82e+00 +/- 5.3e-02  |  1.92e+00 +/- 7.8e-02  |
+test_perturb_1                          |     -5.34 +/- 0.99     | -6.44e-01 +/- 1.20e-01 |  1.14e+01 +/- 7.1e-02  |  1.21e+01 +/- 9.7e-02  |
 test_perturb_2                          |     -5.51 +/- 2.15     | -9.34e-01 +/- 3.64e-01 |  1.60e+01 +/- 3.4e-01  |  1.70e+01 +/- 1.3e-01  |
-test_proximal_jac_atf                   |     +3.80 +/- 1.14     | +2.95e-01 +/- 8.87e-02 |  8.05e+00 +/- 2.6e-02  |  7.75e+00 +/- 8.5e-02  |
 test_proximal_freeb_compute             |     +4.66 +/- 3.47     | +7.98e-03 +/- 5.95e-03 |  1.79e-01 +/- 7.6e-04  |  1.71e-01 +/- 5.9e-03  |
-test_proximal_freeb_jac                 |     +3.85 +/- 1.26     | +2.72e-01 +/- 8.88e-02 |  7.33e+00 +/- 5.8e-02  |  7.06e+00 +/- 6.7e-02  |
 test_solve_fixed_iter                   |     +2.95 +/- 60.45    | +1.39e-01 +/- 2.85e+00 |  4.85e+00 +/- 2.0e+00  |  4.72e+00 +/- 2.0e+00  |

[codecov]

Codecov Report

Attention: Patch coverage is 78.57143% with 3 lines in your changes missing coverage. Please review.

Project coverage is 95.33%. Comparing base (f9469d2) to head (7f93cea).
Report is 34 commits behind head on master.

Files	Patch %	Lines
desc/equilibrium/coords.py	76.92%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1188      +/-   ##
==========================================
- Coverage   95.42%   95.33%   -0.10%     
==========================================
  Files          90       90              
  Lines       22576    22581       +5     
==========================================
- Hits        21544    21527      -17     
- Misses       1032     1054      +22     

Files	Coverage Δ
desc/grid.py	92.89% <100.00%> (ø)
desc/equilibrium/coords.py	83.93% <76.92%> (-7.87%)	⬇️

... and 1 file with indirect coverage changes

[dpanici]

Merge #1175 first

[unalmis]

My bad for making multiple commits that should have been one. I'm done committing now.

[rahulgaur104]

Is iota_r being used anywhere or is it just there so you can use Hermite?

[unalmis]

iota and iota_r get computed on QuadratureGrid then we use those values to construct Hermite spline for $\iota(\rho)$. $\iota(\rho)$ is then evaluated at whatever sequence of $\rho$ values the Newton iteration proceeds with. For $\rho, \alpha, \zeta$ coordinate mappings, the $\rho$ values don't need to change throughout Newton iteration since we can just do 1D root finding, which this PR now ensures is done.