Using quadrature grid for the normalizing length a

[rahulgaur104]

Fixes #1424

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.56%. Comparing base (8af856d) to head (4f7b5ac).
Report is 8 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1430   +/-   ##
=======================================
  Coverage   95.56%   95.56%           
=======================================
  Files          98       98           
  Lines       25115    25115           
=======================================
+ Hits        24000    24002    +2     
+ Misses       1115     1113    -2     

Files with missing lines	Coverage Δ
desc/objectives/_stability.py	98.51% <100.00%> (ø)

... 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         |     -1.88 +/- 6.88     | -1.03e-02 +/- 3.77e-02 |  5.38e-01 +/- 3.5e-02  |  5.49e-01 +/- 1.4e-02  |
 test_equilibrium_init_medres            |     +1.15 +/- 5.45     | +4.83e-02 +/- 2.30e-01 |  4.26e+00 +/- 8.5e-02  |  4.21e+00 +/- 2.1e-01  |
 test_equilibrium_init_highres           |     -1.14 +/- 4.82     | -6.40e-02 +/- 2.71e-01 |  5.56e+00 +/- 1.9e-01  |  5.62e+00 +/- 2.0e-01  |
 test_objective_compile_dshape_current   |     -0.28 +/- 4.08     | -1.12e-02 +/- 1.61e-01 |  3.93e+00 +/- 7.7e-02  |  3.95e+00 +/- 1.4e-01  |
 test_objective_compute_dshape_current   |     -0.68 +/- 2.92     | -2.36e-05 +/- 1.01e-04 |  3.45e-03 +/- 4.8e-05  |  3.47e-03 +/- 8.9e-05  |
 test_objective_jac_dshape_current       |     -1.25 +/- 6.85     | -5.21e-04 +/- 2.85e-03 |  4.11e-02 +/- 2.0e-03  |  4.16e-02 +/- 2.0e-03  |
 test_perturb_2                          |     +3.25 +/- 4.28     | +6.24e-01 +/- 8.23e-01 |  1.98e+01 +/- 5.0e-01  |  1.92e+01 +/- 6.6e-01  |
 test_proximal_freeb_jac                 |     -1.02 +/- 1.38     | -7.55e-02 +/- 1.02e-01 |  7.34e+00 +/- 6.6e-02  |  7.41e+00 +/- 7.8e-02  |
 test_solve_fixed_iter                   |     +1.78 +/- 2.04     | +5.06e-01 +/- 5.81e-01 |  2.90e+01 +/- 4.6e-01  |  2.85e+01 +/- 3.6e-01  |
 test_LinearConstraintProjection_build   |     -0.17 +/- 1.54     | -3.88e-02 +/- 3.53e-01 |  2.28e+01 +/- 1.9e-01  |  2.29e+01 +/- 3.0e-01  |
 test_build_transform_fft_midres         |     +8.33 +/- 4.38     | +5.12e-02 +/- 2.69e-02 |  6.66e-01 +/- 1.9e-02  |  6.15e-01 +/- 1.9e-02  |
 test_build_transform_fft_highres        |     +5.14 +/- 3.46     | +5.04e-02 +/- 3.40e-02 |  1.03e+00 +/- 1.2e-02  |  9.80e-01 +/- 3.2e-02  |
 test_equilibrium_init_lowres            |    +11.63 +/- 4.84     | +4.60e-01 +/- 1.92e-01 |  4.42e+00 +/- 5.2e-02  |  3.96e+00 +/- 1.8e-01  |
 test_objective_compile_atf              |     +6.68 +/- 5.45     | +5.31e-01 +/- 4.33e-01 |  8.48e+00 +/- 2.8e-01  |  7.95e+00 +/- 3.3e-01  |
 test_objective_compute_atf              |    +12.55 +/- 4.41     | +1.27e-03 +/- 4.46e-04 |  1.14e-02 +/- 4.3e-04  |  1.01e-02 +/- 1.0e-04  |
 test_objective_jac_atf                  |     +3.02 +/- 1.89     | +5.88e-02 +/- 3.67e-02 |  2.01e+00 +/- 2.8e-02  |  1.95e+00 +/- 2.4e-02  |
 test_perturb_1                          |     +9.00 +/- 3.81     | +1.28e+00 +/- 5.40e-01 |  1.54e+01 +/- 3.7e-01  |  1.42e+01 +/- 3.9e-01  |
 test_proximal_jac_atf                   |     -0.14 +/- 1.24     | -1.18e-02 +/- 1.01e-01 |  8.19e+00 +/- 4.6e-02  |  8.20e+00 +/- 9.1e-02  |
 test_proximal_freeb_compute             |     +0.86 +/- 0.92     | +1.68e-03 +/- 1.79e-03 |  1.97e-01 +/- 1.5e-03  |  1.95e-01 +/- 9.4e-04  |
 test_solve_fixed_iter_compiled          |     +1.08 +/- 1.41     | +1.83e-01 +/- 2.38e-01 |  1.70e+01 +/- 1.6e-01  |  1.68e+01 +/- 1.7e-01  |

[dpanici]

Approved once comment is updated