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         |     +7.47 +/- 3.51     | +3.86e-02 +/- 1.81e-02 |  5.55e-01 +/- 1.6e-02  |  5.16e-01 +/- 8.8e-03  |
 test_equilibrium_init_medres            |     +5.54 +/- 8.34     | +2.27e-01 +/- 3.42e-01 |  4.33e+00 +/- 3.2e-01  |  4.10e+00 +/- 1.3e-01  |
 test_equilibrium_init_highres           |     -1.03 +/- 2.45     | -5.63e-02 +/- 1.34e-01 |  5.40e+00 +/- 5.4e-02  |  5.45e+00 +/- 1.2e-01  |
 test_objective_compile_dshape_current   |     +1.36 +/- 2.86     | +5.20e-02 +/- 1.09e-01 |  3.86e+00 +/- 6.2e-02  |  3.81e+00 +/- 8.9e-02  |
 test_objective_compute_dshape_current   |     -1.70 +/- 4.28     | -6.20e-05 +/- 1.57e-04 |  3.59e-03 +/- 1.5e-04  |  3.65e-03 +/- 4.6e-05  |
 test_objective_jac_dshape_current       |     -0.12 +/- 8.03     | -4.53e-05 +/- 3.14e-03 |  3.90e-02 +/- 1.9e-03  |  3.91e-02 +/- 2.5e-03  |
 test_perturb_2                          |     +0.86 +/- 4.17     | +1.48e-01 +/- 7.19e-01 |  1.74e+01 +/- 6.6e-01  |  1.73e+01 +/- 2.8e-01  |
 test_proximal_freeb_jac                 |     -0.28 +/- 1.27     | -2.06e-02 +/- 9.39e-02 |  7.40e+00 +/- 6.4e-02  |  7.42e+00 +/- 6.8e-02  |
 test_solve_fixed_iter                   |     +0.79 +/- 61.09    | +3.81e-02 +/- 2.95e+00 |  4.87e+00 +/- 2.0e+00  |  4.84e+00 +/- 2.1e+00  |
 test_build_transform_fft_midres         |     -5.16 +/- 3.33     | -3.55e-02 +/- 2.29e-02 |  6.53e-01 +/- 2.0e-02  |  6.88e-01 +/- 1.1e-02  |
 test_build_transform_fft_highres        |     -3.03 +/- 3.22     | -3.28e-02 +/- 3.49e-02 |  1.05e+00 +/- 1.8e-02  |  1.08e+00 +/- 3.0e-02  |
+test_equilibrium_init_lowres            |     -8.58 +/- 1.85     | -3.83e-01 +/- 8.26e-02 |  4.08e+00 +/- 4.7e-02  |  4.46e+00 +/- 6.8e-02  |
 test_objective_compile_atf              |     -2.42 +/- 2.09     | -2.09e-01 +/- 1.80e-01 |  8.40e+00 +/- 1.4e-01  |  8.61e+00 +/- 1.1e-01  |
 test_objective_compute_atf              |     +2.97 +/- 4.62     | +3.38e-04 +/- 5.25e-04 |  1.17e-02 +/- 4.6e-04  |  1.14e-02 +/- 2.6e-04  |
 test_objective_jac_atf                  |     -1.59 +/- 2.10     | -3.28e-02 +/- 4.33e-02 |  2.03e+00 +/- 3.1e-02  |  2.06e+00 +/- 3.0e-02  |
 test_perturb_1                          |     -5.26 +/- 2.18     | -7.41e-01 +/- 3.07e-01 |  1.33e+01 +/- 1.1e-01  |  1.41e+01 +/- 2.8e-01  |
 test_proximal_jac_atf                   |     -0.42 +/- 1.08     | -3.51e-02 +/- 9.05e-02 |  8.37e+00 +/- 8.0e-02  |  8.40e+00 +/- 4.2e-02  |
 test_proximal_freeb_compute             |     +0.76 +/- 1.13     | +1.44e-03 +/- 2.14e-03 |  1.91e-01 +/- 1.6e-03  |  1.89e-01 +/- 1.4e-03  |

[codecov]

Codecov Report

Attention: Patch coverage is 88.82576% with 59 lines in your changes missing coverage. Please review.

Project coverage is 95.30%. Comparing base (75eafcc) to head (fd7b381).

Files with missing lines	Patch %	Lines
desc/objectives/nae_utils.py	91.85%	39 Missing ⚠️
desc/equilibrium/equilibrium.py	44.11%	19 Missing ⚠️
desc/objectives/getters.py	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1036      +/-   ##
==========================================
- Coverage   95.44%   95.30%   -0.15%     
==========================================
  Files          95       95              
  Lines       23423    23926     +503     
==========================================
+ Hits        22357    22803     +446     
- Misses       1066     1123      +57     

Flag	Coverage Δ
	95.30% <88.82%> (?)

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Files with missing lines	Coverage Δ
desc/objectives/linear_objectives.py	97.05% <100.00%> (+<0.01%)	⬆️
desc/objectives/utils.py	100.00% <ø> (ø)
desc/objectives/getters.py	95.18% <80.00%> (+0.11%)	⬆️
desc/equilibrium/equilibrium.py	93.29% <44.11%> (-2.43%)	⬇️
desc/objectives/nae_utils.py	93.50% <91.85%> (-3.72%)	⬇️

... and 1 file with indirect coverage changes