CDP CD player SLICOT Working note 2002-2 Y. Chahlaoui, P. Van Dooren --> Ex. 2.3 W. Draijer, M. Steinbuch, O.H. Bosgra and "Adaptive control of the radial servo system of a compact disc player" Automatica, Vol. 28, No. 3, pp. 455-462, 1992
simulation.py
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:54:03).
import numpy as np
import system_model
from scipy.integrate import solve_ivp, odeint
from ackrep_core import ResultContainer
from ackrep_core.system_model_management import save_plot_in_dir
import matplotlib.pyplot as plt
import os
from ipydex import Container
# link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
def simulate():
"""
simulate the system model with scipy.integrate.solve_ivp
:return: result of solve_ivp, might contains input function
"""
model = system_model.Model()
rhs_xx_pp_symb = model.get_rhs_symbolic()
rhs = model.get_rhs_func()
# initial state values
xx0 = np.ones(model.sys_dim)
t_end = 10
tt = np.linspace(0, t_end, 1000)
simulation_data = solve_ivp(rhs, (0, t_end), xx0, t_eval=tt)
# using odeint for models with large state vectors
# res = odeint(rhs, y0=xx0, t=tt, tfirst=True)
# simulation_data = Container()
# simulation_data.y = res.transpose()
# simulation_data.t = tt
# postprocessing: calc output
ny = 2
C = model.get_parameter_value("C")
D21 = model.get_parameter_value("D21")
output = np.zeros((ny, len(tt)))
for i in range(len(tt)):
output[:,i] = np.matmul(C, simulation_data.y[:,i]) # + np.matmul(D21, w)
simulation_data.output = output
save_plot(simulation_data)
return simulation_data
def save_plot(simulation_data):
"""
plot your data and save the plot
access to data via: simulation_data.t array of time values
simulation_data.y array of data components
simulation_data.uu array of input values
:param simulation_data: simulation_data of system_model
:return: None
"""
for i in range(simulation_data.output.shape[0]):
plt.plot(simulation_data.t, simulation_data.output[i], label=f"$y_{i}$")
plt.legend()
plt.tight_layout()
save_plot_in_dir()
def evaluate_simulation(simulation_data):
"""
assert that the simulation results are as expected
:param simulation_data: simulation_data of system_model
:return:
"""
expected_final_state = np.zeros(120)
rc = ResultContainer(score=1.0)
simulated_final_state = simulation_data.y[:, -1]
rc.final_state_errors = [
simulated_final_state[i] - expected_final_state[i] for i in np.arange(0, len(simulated_final_state))
]
rc.success = np.allclose(expected_final_state, simulated_final_state, rtol=0, atol=1e-2)
return rc
system_model.py
# This file was autogenerated from the template: system_model.py.template (2022-10-10 15:54:03).
import sympy as sp
import numpy as np
import symbtools as st
import importlib
import sys, os
#from ipydex import IPS, activate_ips_on_exception
from ackrep_core.system_model_management import GenericModel, import_parameters
# Import parameter_file
params = import_parameters()
#link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
class Model(GenericModel):
def initialize(self):
"""
this function is called by the constructor of GenericModel
:return: None
"""
# Define number of inputs -- MODEL DEPENDENT
self.u_dim = 2
# Set "sys_dim" to constant value, if system dimension is constant
self.sys_dim = 120
# check existence of params file
self.has_params = True
self.params = params
# ----------- SET DEFAULT INPUT FUNCTION ---------- #
def uu_default_func(self):
"""
define input function
:return:(function with 2 args - t, xx_nv) default input function
"""
def uu_rhs(t, xx_nv):
"""
sequence of numerical input values
:param t:(scalar or vector) time
:param xx_nv:(vector or array of vectors) numeric state vector
:return:(list) numeric inputs
"""
u = np.zeros(self.u_dim)
return u
return uu_rhs
# ----------- SYMBOLIC RHS FUNCTION ---------- #
def get_rhs_symbolic(self):
"""
define symbolic rhs function
:return: matrix of symbolic rhs-functions
"""
if self.dxx_dt_symb is not None:
return self.dxx_dt_symb
x = self.xx_symb
A, B, B1, C1, C, D11, D12, D21 = self.pp_symb # parameters
w = np.zeros(2) # noise
u = self.uu_symb # inputs
# define symbolic rhs functions
self.dxx_dt_symb = np.matmul(A,x) + np.matmul(B1,w) + np.matmul(B,u)
return self.dxx_dt_symb
parameters.py
# This file was autogenerated from the template: parameters.py.template (2022-10-10 15:54:03).
import sys
import os
import numpy as np
import sympy as sp
import tabulate as tab
#link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
# set model name
model_name = 'CD player SLICOT Working note 2002-2'
# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 120, 120)
B = sp.MatrixSymbol('B', 120, 2)
B1 = sp.MatrixSymbol('B1', 120, 2)
C1 = sp.MatrixSymbol('C1', 4, 120)
C = sp.MatrixSymbol('C', 2, 120)
D11 = sp.MatrixSymbol('D11', 4, 2)
D12 = sp.MatrixSymbol('D12', 4, 2)
D21 = sp.MatrixSymbol('D21', 2, 2)
pp_symb = [A, B, B1, C1, C, D11, D12, D21]
# ---------- create auxiliary symbolic parameters
# set numerical values of auxiliary parameters
# trailing "_nv" stands for "numerical value"
A_nv = sp.Matrix(np.array([[-4.33151052e+02, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
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0.00000000e+00, 0.00000000e+00, 3.86737751e+04,
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
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0.00000000e+00, -7.86210672e+02, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
4.00369838e+04, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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0.00000000e+00, 0.00000000e+00, -8.00895393e+02,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
-4.00561650e+02, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 4.21804019e+04, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, -4.21822669e+02, 0.00000000e+00],
[ 4.33129284e+04, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, -4.33151052e+02]]))
B_nv = sp.Matrix(np.array([[ 0.00000000e+00, -9.39879347e-18],
[ 0.00000000e+00, -5.54770249e-18],
[ 0.00000000e+00, -5.18778387e-22],
[ 0.00000000e+00, -3.98474965e-20],
[ 0.00000000e+00, 5.09544025e-19],
[ 0.00000000e+00, 1.10990540e-18],
[ 0.00000000e+00, 4.11273953e-21],
[ 0.00000000e+00, -1.67985134e-18],
[ 0.00000000e+00, 1.07596446e-21],
[ 0.00000000e+00, 1.41798482e-18],
[ 0.00000000e+00, 1.83660291e-21],
[ 0.00000000e+00, -2.16961899e-20],
[ 0.00000000e+00, 1.77150081e-17],
[ 0.00000000e+00, -2.56348193e-18],
[ 0.00000000e+00, 4.20477464e-18],
[ 0.00000000e+00, 2.61348495e-21],
[ 0.00000000e+00, -1.15624373e-18],
[ 0.00000000e+00, 5.51746353e-19],
[ 0.00000000e+00, -7.62425907e-16],
[ 0.00000000e+00, 2.07359101e-18],
[ 0.00000000e+00, -2.92628571e-22],
[ 0.00000000e+00, -1.55229629e-17],
[ 0.00000000e+00, -3.32882049e-21],
[ 0.00000000e+00, 1.66697492e-21],
[ 0.00000000e+00, 3.86347889e-18],
[ 0.00000000e+00, -1.54478564e-17],
[ 0.00000000e+00, -8.37276167e-19],
[ 0.00000000e+00, 3.09149504e-19],
[ 0.00000000e+00, 2.06533885e-18],
[ 0.00000000e+00, -8.22994806e-19],
[ 0.00000000e+00, 8.91222243e-19],
[ 0.00000000e+00, 6.31088870e-18],
[ 0.00000000e+00, -2.36979498e-16],
[ 0.00000000e+00, 3.18740773e-18],
[ 0.00000000e+00, -3.34811379e-20],
[ 0.00000000e+00, 1.60367751e-16],
[ 0.00000000e+00, -4.18248475e-17],
[ 0.00000000e+00, 6.85169481e-18],
[ 0.00000000e+00, -1.87037253e-19],
[ 0.00000000e+00, 3.83354434e-21],
[ 0.00000000e+00, 1.25329112e-17],
[ 0.00000000e+00, 1.60265707e-18],
[ 0.00000000e+00, -2.86421169e-17],
[ 0.00000000e+00, -7.02843055e-18],
[ 0.00000000e+00, 2.81801982e-16],
[ 0.00000000e+00, -6.62394949e-18],
[ 0.00000000e+00, -6.13589666e-16],
[ 0.00000000e+00, 6.90140930e-17],
[ 0.00000000e+00, -5.85060626e-17],
[ 0.00000000e+00, -8.32940765e-18],
[ 0.00000000e+00, 7.58392221e-16],
[ 0.00000000e+00, -1.30932622e-14],
[ 0.00000000e+00, -9.70144054e-19],
[ 0.00000000e+00, 2.36868123e-17],
[ 0.00000000e+00, 1.06005922e-16],
[ 0.00000000e+00, 6.10735159e-18],
[ 0.00000000e+00, -1.77431401e-17],
[ 0.00000000e+00, -1.81902034e-18],
[ 0.00000000e+00, 4.84518197e-22],
[ 0.00000000e+00, -1.16240230e-22],
[ 3.56006179e-02, -9.49204862e-07],
[ 1.02332255e+03, -3.95652199e-06],
[ 5.39561280e+00, 1.18282601e-01],
[ 1.74373244e+01, -1.44888519e-01],
[ 6.31360705e+00, 2.14960856e-01],
[ 1.02646620e+01, -8.65632635e-01],
[ 5.79866050e+01, -1.93423888e-01],
[ 9.31966931e+01, 2.38855105e-01],
[ 9.31933343e+00, -1.06918131e+02],
[ 1.46905145e+00, 2.86961453e+02],
[ 4.59011804e+01, 7.94423571e-01],
[ 1.47380016e+01, -4.77754034e-01],
[ 1.13420721e+01, 8.42168537e-01],
[ 1.21214456e+01, -5.01050533e+00],
[ 2.48587659e-01, 1.52698223e+00],
[ 5.65818644e+00, -2.30116380e+00],
[ 2.80191809e-02, -5.73933863e-02],
[ 2.28687984e-02, -2.33888358e-01],
[ 2.60509290e-01, -1.30871203e-02],
[ 5.65518852e-03, -1.02342366e-01],
[ 8.74195562e-02, 2.09176050e-03],
[ 5.89739274e-02, -1.52732552e-03],
[ 3.15461659e+00, 2.55128248e+00],
[ 8.88386947e+00, -3.41537078e-01],
[ 2.39352642e+00, -1.30954531e+00],
[ 4.70413874e-02, 3.77214592e-02],
[ 8.14030816e-02, -2.60280189e-02],
[ 2.48347096e-01, -1.93514836e+00],
[ 2.90462422e-01, -5.15340189e-02],
[ 6.16267371e+00, 2.91661480e-01],
[ 5.36438602e+00, 3.38468698e-01],
[ 6.10038047e+00, -1.68653285e-02],
[ 3.74068360e-01, 5.82592267e-01],
[ 1.62725087e+00, 4.89430801e-01],
[ 5.27661569e-01, -1.26145487e-01],
[ 1.49245678e-01, -3.15487412e-02],
[ 7.33395359e-04, -1.36123328e-05],
[ 8.31653610e-02, 1.30570175e-01],
[ 3.11237312e+00, -1.26758797e-01],
[ 9.24815805e+00, 8.65874279e-05],
[ 2.28416880e+00, -1.69327148e-02],
[ 3.89378844e-01, -6.22588560e+00],
[ 2.73496393e+00, 2.28751471e-01],
[ 1.19334241e+00, -9.44175838e-03],
[ 2.79154731e+01, 7.42940039e-03],
[ 2.83268305e+00, -3.43357245e-02],
[ 8.62207795e-01, 5.99359259e-01],
[ 1.68507529e+00, -1.44658796e-01],
[ 1.66975576e+00, 3.92101557e-02],
[ 6.97811448e-01, 2.51468511e-03],
[ 1.33584410e+00, -1.15791072e-02],
[ 4.80264483e-01, 2.06765631e-04],
[ 1.81437022e+00, -1.37174802e-02],
[ 5.62240195e-02, 8.11281345e-04],
[ 4.28178299e-01, -9.06336474e-03],
[ 1.78345910e+00, -4.16088013e-03],
[ 6.81942697e-01, -3.25390248e-04],
[ 9.59865096e-01, 6.96280097e-04],
[ 1.27248177e+00, -4.53019247e-02],
[ 1.41190333e-02, 4.16366336e+00]]))
B1_nv = sp.Matrix(np.array([[ 0.00000000e+00, -9.39879347e-18],
[ 0.00000000e+00, -5.54770249e-18],
[ 0.00000000e+00, -5.18778387e-22],
[ 0.00000000e+00, -3.98474965e-20],
[ 0.00000000e+00, 5.09544025e-19],
[ 0.00000000e+00, 1.10990540e-18],
[ 0.00000000e+00, 4.11273953e-21],
[ 0.00000000e+00, -1.67985134e-18],
[ 0.00000000e+00, 1.07596446e-21],
[ 0.00000000e+00, 1.41798482e-18],
[ 0.00000000e+00, 1.83660291e-21],
[ 0.00000000e+00, -2.16961899e-20],
[ 0.00000000e+00, 1.77150081e-17],
[ 0.00000000e+00, -2.56348193e-18],
[ 0.00000000e+00, 4.20477464e-18],
[ 0.00000000e+00, 2.61348495e-21],
[ 0.00000000e+00, -1.15624373e-18],
[ 0.00000000e+00, 5.51746353e-19],
[ 0.00000000e+00, -7.62425907e-16],
[ 0.00000000e+00, 2.07359101e-18],
[ 0.00000000e+00, -2.92628571e-22],
[ 0.00000000e+00, -1.55229629e-17],
[ 0.00000000e+00, -3.32882049e-21],
[ 0.00000000e+00, 1.66697492e-21],
[ 0.00000000e+00, 3.86347889e-18],
[ 0.00000000e+00, -1.54478564e-17],
[ 0.00000000e+00, -8.37276167e-19],
[ 0.00000000e+00, 3.09149504e-19],
[ 0.00000000e+00, 2.06533885e-18],
[ 0.00000000e+00, -8.22994806e-19],
[ 0.00000000e+00, 8.91222243e-19],
[ 0.00000000e+00, 6.31088870e-18],
[ 0.00000000e+00, -2.36979498e-16],
[ 0.00000000e+00, 3.18740773e-18],
[ 0.00000000e+00, -3.34811379e-20],
[ 0.00000000e+00, 1.60367751e-16],
[ 0.00000000e+00, -4.18248475e-17],
[ 0.00000000e+00, 6.85169481e-18],
[ 0.00000000e+00, -1.87037253e-19],
[ 0.00000000e+00, 3.83354434e-21],
[ 0.00000000e+00, 1.25329112e-17],
[ 0.00000000e+00, 1.60265707e-18],
[ 0.00000000e+00, -2.86421169e-17],
[ 0.00000000e+00, -7.02843055e-18],
[ 0.00000000e+00, 2.81801982e-16],
[ 0.00000000e+00, -6.62394949e-18],
[ 0.00000000e+00, -6.13589666e-16],
[ 0.00000000e+00, 6.90140930e-17],
[ 0.00000000e+00, -5.85060626e-17],
[ 0.00000000e+00, -8.32940765e-18],
[ 0.00000000e+00, 7.58392221e-16],
[ 0.00000000e+00, -1.30932622e-14],
[ 0.00000000e+00, -9.70144054e-19],
[ 0.00000000e+00, 2.36868123e-17],
[ 0.00000000e+00, 1.06005922e-16],
[ 0.00000000e+00, 6.10735159e-18],
[ 0.00000000e+00, -1.77431401e-17],
[ 0.00000000e+00, -1.81902034e-18],
[ 0.00000000e+00, 4.84518197e-22],
[ 0.00000000e+00, -1.16240230e-22],
[ 3.56006179e-02, -9.49204862e-07],
[ 1.02332255e+03, -3.95652199e-06],
[ 5.39561280e+00, 1.18282601e-01],
[ 1.74373244e+01, -1.44888519e-01],
[ 6.31360705e+00, 2.14960856e-01],
[ 1.02646620e+01, -8.65632635e-01],
[ 5.79866050e+01, -1.93423888e-01],
[ 9.31966931e+01, 2.38855105e-01],
[ 9.31933343e+00, -1.06918131e+02],
[ 1.46905145e+00, 2.86961453e+02],
[ 4.59011804e+01, 7.94423571e-01],
[ 1.47380016e+01, -4.77754034e-01],
[ 1.13420721e+01, 8.42168537e-01],
[ 1.21214456e+01, -5.01050533e+00],
[ 2.48587659e-01, 1.52698223e+00],
[ 5.65818644e+00, -2.30116380e+00],
[ 2.80191809e-02, -5.73933863e-02],
[ 2.28687984e-02, -2.33888358e-01],
[ 2.60509290e-01, -1.30871203e-02],
[ 5.65518852e-03, -1.02342366e-01],
[ 8.74195562e-02, 2.09176050e-03],
[ 5.89739274e-02, -1.52732552e-03],
[ 3.15461659e+00, 2.55128248e+00],
[ 8.88386947e+00, -3.41537078e-01],
[ 2.39352642e+00, -1.30954531e+00],
[ 4.70413874e-02, 3.77214592e-02],
[ 8.14030816e-02, -2.60280189e-02],
[ 2.48347096e-01, -1.93514836e+00],
[ 2.90462422e-01, -5.15340189e-02],
[ 6.16267371e+00, 2.91661480e-01],
[ 5.36438602e+00, 3.38468698e-01],
[ 6.10038047e+00, -1.68653285e-02],
[ 3.74068360e-01, 5.82592267e-01],
[ 1.62725087e+00, 4.89430801e-01],
[ 5.27661569e-01, -1.26145487e-01],
[ 1.49245678e-01, -3.15487412e-02],
[ 7.33395359e-04, -1.36123328e-05],
[ 8.31653610e-02, 1.30570175e-01],
[ 3.11237312e+00, -1.26758797e-01],
[ 9.24815805e+00, 8.65874279e-05],
[ 2.28416880e+00, -1.69327148e-02],
[ 3.89378844e-01, -6.22588560e+00],
[ 2.73496393e+00, 2.28751471e-01],
[ 1.19334241e+00, -9.44175838e-03],
[ 2.79154731e+01, 7.42940039e-03],
[ 2.83268305e+00, -3.43357245e-02],
[ 8.62207795e-01, 5.99359259e-01],
[ 1.68507529e+00, -1.44658796e-01],
[ 1.66975576e+00, 3.92101557e-02],
[ 6.97811448e-01, 2.51468511e-03],
[ 1.33584410e+00, -1.15791072e-02],
[ 4.80264483e-01, 2.06765631e-04],
[ 1.81437022e+00, -1.37174802e-02],
[ 5.62240195e-02, 8.11281345e-04],
[ 4.28178299e-01, -9.06336474e-03],
[ 1.78345910e+00, -4.16088013e-03],
[ 6.81942697e-01, -3.25390248e-04],
[ 9.59865096e-01, 6.96280097e-04],
[ 1.27248177e+00, -4.53019247e-02],
[ 1.41190333e-02, 4.16366336e+00]]))
C1_nv = sp.Matrix(np.array([[ 4.16357134e+00, -1.70980649e-01, 9.59816666e-01,
-5.69889254e-01, -3.31886737e-01, 4.44868342e-04,
-3.68419187e-02, 1.81442179e+00, -1.04459087e-01,
3.51252554e-01, 9.43814104e-02, 1.52903946e+00,
-1.67365839e+00, -1.04974623e+00, -2.11626606e-01,
2.79154740e+01, 7.69237929e-02, -4.55042081e-01,
6.23405846e+00, 2.31598414e-03, 9.24815805e+00,
-1.05750952e-01, -2.17235054e-02, 7.08881458e-04,
1.52597373e-04, -3.97763322e-04, 2.62583032e-01,
-6.59149461e-01, 4.59838662e+00, -4.00891699e+00,
5.20662831e+00, 2.37655003e-01, 8.27402119e-01,
1.09805310e-03, 2.42987161e-04, 8.26618370e-02,
9.05548641e-01, 4.86869077e-01, -1.26512717e-03,
6.51604200e-05, -1.88861269e-04, 1.03856991e-04,
-5.56233278e-04, -1.21424411e-04, -5.38273172e+00,
-6.61625523e-01, -7.24961710e+00, -1.05363842e+01,
-6.75431261e+00, 4.59043750e+01, -5.91748637e+00,
-1.02014035e+01, -9.16768156e+01, -5.64541558e+01,
-2.09222808e+00, -1.71363181e+00, -1.36966281e+01,
-5.33563105e+00, -1.02332255e+03, 3.56006179e-02,
-4.35418827e-18, -1.26477232e-13, -6.16680118e-17,
1.16054766e-15, 2.48207250e-17, -2.74296671e-16,
-5.39110129e-15, -2.28108303e-15, 1.05859081e-15,
3.68666963e-17, 3.97220619e-15, 5.92679508e-16,
1.13602349e-15, 8.64225876e-16, -2.71110127e-18,
-6.65802278e-16, 1.44113899e-20, 6.66341444e-20,
1.21531829e-20, -2.30708780e-20, 2.38505098e-22,
1.50359351e-19, -1.10133419e-18, -1.08856959e-16,
1.00172060e-17, 2.72869627e-22, 1.31929023e-19,
-1.02097799e-16, 2.89243262e-17, -4.66507138e-18,
-7.76232426e-18, 5.60179062e-16, 6.45579817e-19,
-2.21925159e-19, 4.70828823e-20, 1.86492570e-20,
8.69172494e-20, -9.17370287e-20, 1.30300392e-17,
2.44933629e-17, 2.78313780e-19, -7.47314419e-16,
2.06437816e-18, -8.88752560e-18, -3.85215265e-17,
-2.57800964e-17, -3.36548345e-18, -2.01443856e-16,
1.67166728e-18, 2.04508367e-19, 4.27982404e-17,
9.22011894e-20, -2.23055546e-16, 1.49431376e-19,
5.49537938e-20, -4.16806611e-17, 6.72277463e-17,
1.21380290e-18, 2.08646391e-17, 6.75335096e-18],
[ 3.10750290e-02, -1.26175582e+00, 9.66717877e-03,
3.74529286e-01, 1.75231130e+00, 4.28273980e-01,
4.24790721e-02, -1.02331228e-03, 4.68766803e-01,
-1.28888913e+00, 6.91403855e-01, -6.72056615e-01,
2.43459440e-01, -2.58197922e-02, -2.82497547e+00,
1.78187354e-03, 1.19089797e+00, 2.70652759e+00,
-2.23119988e-01, -2.28423039e+00, -1.65770226e-04,
3.11315771e+00, 1.53274712e-01, 1.88523544e-04,
-1.52543673e-01, -5.42530420e-01, 1.67885021e+00,
-2.11808582e-01, 4.00871137e+00, -3.58047246e+00,
3.30977874e+00, 1.74769200e-01, 1.76688460e+00,
8.54559169e-02, -6.02971108e-02, 2.72709455e+00,
-8.84419391e+00, -4.02785385e+00, 5.89801347e-02,
-8.74445540e-02, 1.02498319e-01, -2.60837789e-01,
-2.35003056e-01, -6.38675234e-02, -2.88732191e+00,
-1.39847139e+00, 1.09305836e+01, 4.28210870e+00,
-1.31078680e+01, -5.81224937e-01, 2.86904195e+02,
-1.06837578e+02, 1.67643113e+01, -1.32443224e+01,
-1.00863863e+01, 6.08040361e+00, -1.07927592e+01,
-8.10968290e-01, 8.26923657e-03, -2.04568943e-06,
2.45681258e-22, 1.01298497e-18, -1.93251218e-17,
1.06826931e-15, -1.06559904e-16, -1.31618856e-15,
-1.21595867e-15, 3.60048511e-16, 1.14318663e-14,
-1.02685296e-15, 6.35363647e-18, 9.48218180e-16,
-4.34231722e-16, -1.29788859e-15, -9.26587107e-18,
-3.55357979e-16, 7.57709588e-18, 2.84415278e-17,
-3.13255182e-17, 1.22941206e-17, -3.03868816e-19,
-6.97186762e-18, 8.28337195e-18, 1.04032792e-15,
3.28650075e-16, -4.65327724e-20, 1.01862510e-17,
-2.22807939e-16, 2.11239821e-17, -5.36984878e-18,
4.36855474e-18, 4.87066149e-16, 1.45189312e-19,
-1.75274649e-18, 6.54882533e-17, -1.86115742e-17,
2.30448313e-20, 6.32823409e-19, -3.83403398e-16,
-3.49281183e-22, -2.70978721e-16, 2.71494970e-17,
-1.31944408e-17, -1.42305015e-16, -7.70223576e-21,
-3.36768692e-16, 2.45311463e-20, 2.91527374e-17,
-4.32160388e-19, -1.51671565e-19, -1.56680307e-16,
1.34055797e-18, 1.25404183e-19, -1.01883609e-19,
5.29734131e-17, 2.22412352e-16, -4.60494930e-17,
1.66492995e-20, 1.53895314e-16, 5.13448565e-20],
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]))
C_nv = sp.Matrix(np.array([[ 4.16357134e+00, -1.70980649e-01, 9.59816666e-01,
-5.69889254e-01, -3.31886737e-01, 4.44868342e-04,
-3.68419187e-02, 1.81442179e+00, -1.04459087e-01,
3.51252554e-01, 9.43814104e-02, 1.52903946e+00,
-1.67365839e+00, -1.04974623e+00, -2.11626606e-01,
2.79154740e+01, 7.69237929e-02, -4.55042081e-01,
6.23405846e+00, 2.31598414e-03, 9.24815805e+00,
-1.05750952e-01, -2.17235054e-02, 7.08881458e-04,
1.52597373e-04, -3.97763322e-04, 2.62583032e-01,
-6.59149461e-01, 4.59838662e+00, -4.00891699e+00,
5.20662831e+00, 2.37655003e-01, 8.27402119e-01,
1.09805310e-03, 2.42987161e-04, 8.26618370e-02,
9.05548641e-01, 4.86869077e-01, -1.26512717e-03,
6.51604200e-05, -1.88861269e-04, 1.03856991e-04,
-5.56233278e-04, -1.21424411e-04, -5.38273172e+00,
-6.61625523e-01, -7.24961710e+00, -1.05363842e+01,
-6.75431261e+00, 4.59043750e+01, -5.91748637e+00,
-1.02014035e+01, -9.16768156e+01, -5.64541558e+01,
-2.09222808e+00, -1.71363181e+00, -1.36966281e+01,
-5.33563105e+00, -1.02332255e+03, 3.56006179e-02,
-4.35418827e-18, -1.26477232e-13, -6.16680118e-17,
1.16054766e-15, 2.48207250e-17, -2.74296671e-16,
-5.39110129e-15, -2.28108303e-15, 1.05859081e-15,
3.68666963e-17, 3.97220619e-15, 5.92679508e-16,
1.13602349e-15, 8.64225876e-16, -2.71110127e-18,
-6.65802278e-16, 1.44113899e-20, 6.66341444e-20,
1.21531829e-20, -2.30708780e-20, 2.38505098e-22,
1.50359351e-19, -1.10133419e-18, -1.08856959e-16,
1.00172060e-17, 2.72869627e-22, 1.31929023e-19,
-1.02097799e-16, 2.89243262e-17, -4.66507138e-18,
-7.76232426e-18, 5.60179062e-16, 6.45579817e-19,
-2.21925159e-19, 4.70828823e-20, 1.86492570e-20,
8.69172494e-20, -9.17370287e-20, 1.30300392e-17,
2.44933629e-17, 2.78313780e-19, -7.47314419e-16,
2.06437816e-18, -8.88752560e-18, -3.85215265e-17,
-2.57800964e-17, -3.36548345e-18, -2.01443856e-16,
1.67166728e-18, 2.04508367e-19, 4.27982404e-17,
9.22011894e-20, -2.23055546e-16, 1.49431376e-19,
5.49537938e-20, -4.16806611e-17, 6.72277463e-17,
1.21380290e-18, 2.08646391e-17, 6.75335096e-18],
[ 3.10750290e-02, -1.26175582e+00, 9.66717877e-03,
3.74529286e-01, 1.75231130e+00, 4.28273980e-01,
4.24790721e-02, -1.02331228e-03, 4.68766803e-01,
-1.28888913e+00, 6.91403855e-01, -6.72056615e-01,
2.43459440e-01, -2.58197922e-02, -2.82497547e+00,
1.78187354e-03, 1.19089797e+00, 2.70652759e+00,
-2.23119988e-01, -2.28423039e+00, -1.65770226e-04,
3.11315771e+00, 1.53274712e-01, 1.88523544e-04,
-1.52543673e-01, -5.42530420e-01, 1.67885021e+00,
-2.11808582e-01, 4.00871137e+00, -3.58047246e+00,
3.30977874e+00, 1.74769200e-01, 1.76688460e+00,
8.54559169e-02, -6.02971108e-02, 2.72709455e+00,
-8.84419391e+00, -4.02785385e+00, 5.89801347e-02,
-8.74445540e-02, 1.02498319e-01, -2.60837789e-01,
-2.35003056e-01, -6.38675234e-02, -2.88732191e+00,
-1.39847139e+00, 1.09305836e+01, 4.28210870e+00,
-1.31078680e+01, -5.81224937e-01, 2.86904195e+02,
-1.06837578e+02, 1.67643113e+01, -1.32443224e+01,
-1.00863863e+01, 6.08040361e+00, -1.07927592e+01,
-8.10968290e-01, 8.26923657e-03, -2.04568943e-06,
2.45681258e-22, 1.01298497e-18, -1.93251218e-17,
1.06826931e-15, -1.06559904e-16, -1.31618856e-15,
-1.21595867e-15, 3.60048511e-16, 1.14318663e-14,
-1.02685296e-15, 6.35363647e-18, 9.48218180e-16,
-4.34231722e-16, -1.29788859e-15, -9.26587107e-18,
-3.55357979e-16, 7.57709588e-18, 2.84415278e-17,
-3.13255182e-17, 1.22941206e-17, -3.03868816e-19,
-6.97186762e-18, 8.28337195e-18, 1.04032792e-15,
3.28650075e-16, -4.65327724e-20, 1.01862510e-17,
-2.22807939e-16, 2.11239821e-17, -5.36984878e-18,
4.36855474e-18, 4.87066149e-16, 1.45189312e-19,
-1.75274649e-18, 6.54882533e-17, -1.86115742e-17,
2.30448313e-20, 6.32823409e-19, -3.83403398e-16,
-3.49281183e-22, -2.70978721e-16, 2.71494970e-17,
-1.31944408e-17, -1.42305015e-16, -7.70223576e-21,
-3.36768692e-16, 2.45311463e-20, 2.91527374e-17,
-4.32160388e-19, -1.51671565e-19, -1.56680307e-16,
1.34055797e-18, 1.25404183e-19, -1.01883609e-19,
5.29734131e-17, 2.22412352e-16, -4.60494930e-17,
1.66492995e-20, 1.53895314e-16, 5.13448565e-20]]))
D11_nv = sp.Matrix(np.array([[0., 0.],
[0., 0.],
[0., 0.],
[0., 0.]]))
D12_nv = sp.Matrix(np.array([[0. , 0. ],
[0. , 0. ],
[1.41421356, 0. ],
[0. , 1.41421356]]))
D21_nv = sp.Matrix(np.array([[0.e+00, 1.e+00],
[3.e-02, 2.e-05]]))
# ---------- create symbolic parameter functions
# parameter values can be constant/fixed values OR set in relation to other parameters (for example: a = 2*b)
# list of symbolic parameter functions
# tailing "_sf" stands for "symbolic parameter function"
pp_sf = [A_nv, B_nv, B1_nv, C1_nv, C_nv, D11_nv, D12_nv, D21_nv]
# ---------- list for substitution
# -- entries are tuples like: (independent symbolic parameter, numerical value)
pp_subs_list = []
# OPTONAL: Dictionary which defines how certain variables shall be written
# in the table - key: Symbolic Variable, Value: LaTeX Representation/Code
# useful for example for complex variables: {Z: r"\underline{Z}"}
latex_names = {}
# ---------- Define LaTeX table
# Define table header
# DON'T CHANGE FOLLOWING ENTRIES: "Symbol", "Value"
tabular_header = ["Symbol", "Value"]
# Define column text alignments
col_alignment = ["center", "left"]
# Define Entries of all columns before the Symbol-Column
# --- Entries need to be latex code
col_1 = []
# contains all lists of the columns before the "Symbol" Column
# --- Empty list, if there are no columns before the "Symbol" Column
start_columns_list = []
# Define Entries of the columns after the Value-Column
# --- Entries need to be latex code
col_4 = []
# contains all lists of columns after the FIX ENTRIES
# --- Empty list, if there are no columns after the "Value" column
end_columns_list = []