2nd Order NAE Constraints

[dpanici]

• make tests for this
• write out the coefficients in a simpler form (see below)

Simpler way to write coefficients

from qsc import Qsc
import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import fft

name = 'precise QA'
stel = Qsc.from_paper(name)
R0 = stel.R0
Z0 = stel.Z0
dR0 = stel.R0p
ddR0 = stel.R0pp
dZ0 = stel.Z0p
ddZ0 = stel.Z0pp

x1_cos = stel.X1c*stel.normal_cylindrical.transpose()+stel.Y1c*stel.binormal_cylindrical.transpose()
x1_sin = stel.Y1s*stel.binormal_cylindrical.transpose()

x2_0 = stel.X20*stel.normal_cylindrical.transpose()+stel.Y20*stel.binormal_cylindrical.transpose()+stel.Z20*stel.tangent_cylindrical.transpose()
x2_cos = stel.X2c*stel.normal_cylindrical.transpose()+stel.Y2c*stel.binormal_cylindrical.transpose()+stel.Z2c*stel.tangent_cylindrical.transpose()
x2_sin = stel.X2s*stel.normal_cylindrical.transpose()+stel.Y2s*stel.binormal_cylindrical.transpose()+stel.Z2s*stel.tangent_cylindrical.transpose()

X1Rc = x1_cos[0,:]
dX1Rc = np.matmul(stel.d_d_phi, X1Rc)
X1Rs = x1_sin[0,:]
dX1Rs = np.matmul(stel.d_d_phi, X1Rs)
X1thc = x1_cos[1,:]
dX1thc = np.matmul(stel.d_d_phi, X1thc)
X1ths = x1_sin[1,:]
dX1ths = np.matmul(stel.d_d_phi, X1ths)
X1zc = x1_cos[2,:]
dX1zc = np.matmul(stel.d_d_phi, X1zc)
X1zs = x1_sin[2,:]
dX1zs = np.matmul(stel.d_d_phi, X1zs)
X2R0 = x2_0[0,:]
X2th0 = x2_0[1,:]
X2z0 = x2_0[2,:]
X2Rs = x2_sin[0,:]
X2ths = x2_sin[1,:]
X2zs = x2_sin[2,:]
X2Rc = x2_cos[0,:]
X2thc = x2_cos[1,:]
X2zc = x2_cos[2,:]

R1c = X1Rc - dR0/R0*X1thc
R1s = X1Rs - dR0/R0*X1ths

Z1c = X1zc - dZ0/R0*X1thc
Z1s = X1zs - dZ0/R0*X1ths

R20 = X2R0 - dR0**2*(X1thc**2+X1ths**2)/2/R0**3 + 1/4/R0*(X1thc**2 + X1ths**2 - 4*X2th0*dR0 - 2*X1thc*dX1Rc - 2*X1ths*dX1Rs) + \
    1/4/R0**2*(2*X1Rc*X1thc*dR0 + 2*X1Rs*X1ths*dR0 + 2*X1thc*dR0*dX1thc + 2*X1ths*dR0*dX1ths + 3*(X1thc**2+X1ths**2)*ddR0)
R2s = X2Rs - X1thc*X1ths*dR0**2/R0**3 -(2*X2ths*dR0 + X1ths*dX1Rc + X1thc*(-X1ths + dX1Rs))/(2*R0) + \
    (X1Rs*X1thc*dR0 + X1Rc*X1ths*dR0 + X1ths*dR0*dX1thc + X1thc*dR0*dX1ths + X1thc*X1ths*ddR0)/(2*R0**2)
R2c = X2Rc + (-X1thc**2 + X1ths**2)*dR0**2/(2*R0**3)+1/4/R0*(X1thc**2 - X1ths**2 - 4*X2thc*dR0 - \
    2*X1thc*dX1Rc + 2*X1ths*dX1Rs) + 1/4/R0**2*(2*X1Rc*X1thc*dR0 - 2*X1Rs*X1ths*dR0 + 2*X1thc*dR0*dX1thc - \
    2*X1ths*dR0*dX1ths + (X1thc**2-X1ths**2)*ddR0)

Z20 = X2z0 - (X1thc*dX1zc + X1ths*dX1zs + 2*X2th0*dZ0)/2/R0 + \
    (X1Rc*X1thc + X1Rs*X1ths + X1thc*dX1thc + X1ths*dX1ths)*dZ0/2/R0**2 + \
    (X1thc**2 + X1ths**2)*ddZ0/4/R0**2 - (X1thc**2 + X1ths**2)*dR0*dZ0/2/R0**3 

Z2s = X2zs - (X1ths*dX1zc + X1thc*dX1zs + 2*X2ths*dZ0)/2/R0 + \
    ((X1Rs*X1thc + X1Rc*X1ths+ X1ths*dX1thc + X1thc*dX1ths)*dZ0 + X1thc*X1ths*ddZ0)/2/R0**2 - \
    (X1thc*X1ths*dR0*dZ0)/R0**3 

Z2c = X2zc - (X1thc*dX1zc-X1ths*dX1zs+2*X2thc*dZ0)/2/R0 + \
    (X1Rc*X1thc - X1Rs*X1ths + X1thc*dX1thc - X1ths*dX1ths)*dZ0/2/R0**2 - \
    + (X1thc**2 - X1ths**2)*ddZ0/4/R0**2 - (X1thc**2 - X1ths**2)*dR0*dZ0/2/R0**3)

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     +3.98 +/- 6.87     | +2.17e-02 +/- 3.75e-02 |  5.67e-01 +/- 3.0e-02  |  5.45e-01 +/- 2.3e-02  |
 test_equilibrium_init_medres            |     +0.68 +/- 3.96     | +3.03e-02 +/- 1.76e-01 |  4.48e+00 +/- 1.6e-01  |  4.45e+00 +/- 7.8e-02  |
 test_equilibrium_init_highres           |     -2.29 +/- 4.50     | -1.32e-01 +/- 2.60e-01 |  5.64e+00 +/- 2.2e-01  |  5.77e+00 +/- 1.4e-01  |
 test_objective_compile_dshape_current   |     +0.34 +/- 6.30     | +1.36e-02 +/- 2.54e-01 |  4.05e+00 +/- 1.9e-01  |  4.03e+00 +/- 1.6e-01  |
 test_objective_compute_dshape_current   |     -0.48 +/- 2.55     | -2.50e-05 +/- 1.33e-04 |  5.18e-03 +/- 1.1e-04  |  5.21e-03 +/- 8.0e-05  |
 test_objective_jac_dshape_current       |     +0.23 +/- 5.65     | +9.98e-05 +/- 2.44e-03 |  4.32e-02 +/- 1.8e-03  |  4.31e-02 +/- 1.7e-03  |
 test_perturb_2                          |     -1.24 +/- 3.24     | -2.53e-01 +/- 6.61e-01 |  2.02e+01 +/- 3.5e-01  |  2.04e+01 +/- 5.6e-01  |
 test_proximal_freeb_jac                 |     +0.31 +/- 0.70     | +2.27e-02 +/- 5.15e-02 |  7.39e+00 +/- 4.1e-02  |  7.37e+00 +/- 3.1e-02  |
 test_solve_fixed_iter                   |     +2.16 +/- 2.53     | +7.23e-01 +/- 8.48e-01 |  3.43e+01 +/- 6.7e-01  |  3.36e+01 +/- 5.3e-01  |
 test_LinearConstraintProjection_build   |     +0.37 +/- 2.35     | +3.88e-02 +/- 2.47e-01 |  1.05e+01 +/- 1.8e-01  |  1.05e+01 +/- 1.7e-01  |
 test_build_transform_fft_midres         |     +0.07 +/- 3.25     | +4.36e-04 +/- 2.07e-02 |  6.36e-01 +/- 1.7e-02  |  6.35e-01 +/- 1.2e-02  |
 test_build_transform_fft_highres        |     -0.35 +/- 1.73     | -3.52e-03 +/- 1.73e-02 |  9.97e-01 +/- 1.4e-02  |  1.00e+00 +/- 1.0e-02  |
 test_equilibrium_init_lowres            |     +0.47 +/- 1.74     | +1.91e-02 +/- 7.08e-02 |  4.09e+00 +/- 5.5e-02  |  4.07e+00 +/- 4.5e-02  |
 test_objective_compile_atf              |     -0.13 +/- 4.08     | -1.04e-02 +/- 3.36e-01 |  8.22e+00 +/- 2.6e-01  |  8.23e+00 +/- 2.1e-01  |
 test_objective_compute_atf              |     +0.16 +/- 3.44     | +2.61e-05 +/- 5.58e-04 |  1.62e-02 +/- 3.7e-04  |  1.62e-02 +/- 4.2e-04  |
 test_objective_jac_atf                  |     +1.43 +/- 2.12     | +2.78e-02 +/- 4.11e-02 |  1.97e+00 +/- 2.2e-02  |  1.94e+00 +/- 3.5e-02  |
 test_perturb_1                          |     +0.43 +/- 1.45     | +6.56e-02 +/- 2.21e-01 |  1.53e+01 +/- 1.4e-01  |  1.52e+01 +/- 1.7e-01  |
 test_proximal_jac_atf                   |     -0.32 +/- 0.32     | -2.69e-02 +/- 2.69e-02 |  8.27e+00 +/- 2.1e-02  |  8.29e+00 +/- 1.7e-02  |
 test_proximal_freeb_compute             |     -0.85 +/- 0.79     | -1.73e-03 +/- 1.60e-03 |  2.01e-01 +/- 1.2e-03  |  2.03e-01 +/- 1.1e-03  |
 test_solve_fixed_iter_compiled          |     +0.22 +/- 0.95     | +4.85e-02 +/- 2.11e-01 |  2.22e+01 +/- 1.4e-01  |  2.22e+01 +/- 1.5e-01  |

[codecov]

Codecov Report

Attention: Patch coverage is 2.55906% with 495 lines in your changes missing coverage. Please review.

Project coverage is 93.06%. Comparing base (4bfa728) to head (6015f44).
Report is 38 commits behind head on master.

Files with missing lines	Patch %	Lines
desc/objectives/nae_utils.py	1.20%	493 Missing ⚠️
desc/objectives/getters.py	60.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1036      +/-   ##
==========================================
- Coverage   95.60%   93.06%   -2.54%     
==========================================
  Files          98       98              
  Lines       25300    25800     +500     
==========================================
- Hits        24188    24011     -177     
- Misses       1112     1789     +677     

Files with missing lines	Coverage Δ
desc/equilibrium/equilibrium.py	95.66% <100.00%> (-0.41%)	⬇️
desc/objectives/getters.py	94.04% <60.00%> (-1.08%)	⬇️
desc/objectives/nae_utils.py	30.01% <1.20%> (-67.21%)	⬇️

... and 13 files with indirect coverage changes