TL Transmission Line SLICOT Working note 2002-2 Y. Chahlaoui, P. Van Dooren --> Ex. 2.2 W. Draijer, M. Steinbuch, O.H. Bosgra and J.-R. Li and J. White, "Efficient Model Reduction of Inter- connect via Approximate System Gramians", IEEE, 0-7803-5832-5/99, 1999 Note Ex'=Ax+Bu y=Cx given
simulation.py
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:54:02).
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(256)
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 15:54:02).
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 = 256
# 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(256) # 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 15:54:02).
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 = 'Transmission Line SLICOT Working note 2002-2'
# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 256, 256)
B = sp.MatrixSymbol('B', 256, 2)
B1 = sp.MatrixSymbol('B1', 256, 256)
C1 = sp.MatrixSymbol('C1', 256, 256)
C = sp.MatrixSymbol('C', 2, 256)
D11 = sp.MatrixSymbol('D11', 256, 256)
D12 = sp.MatrixSymbol('D12', 256, 2)
D21 = sp.MatrixSymbol('D21', 2, 256)
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([[-1.04780036e+14, -3.61714243e+05, 8.15234903e+11,
3.99874267e+05, -7.80135772e+11, -1.91625182e+05,
7.23073304e+11, -5.71512328e+05, -6.37976471e+11,
4.09200360e+05, 5.21824071e+11, 8.41864849e+04,
-3.72021649e+11, 3.62511438e+04, 1.94419533e+11,
4.69993742e+05, -7.69906187e+08, 1.08059633e+09,
-2.53047220e+08, 1.16011480e+09, -1.28391586e+09,
-1.25419989e+09, 2.34387682e+07, 1.83097467e+09,
1.62276995e+09, 1.22747646e+09, 2.27372079e+09,
-1.61774938e+09, 1.54848984e+09, -4.40995466e+09,
-1.15645411e+09, 1.66668424e+09, -1.23900005e+09,
7.51677240e+08, -4.85089068e+08, -4.06463878e+09,
-2.06800225e+09, 1.85568914e+09, 1.46937660e+08,
6.37524166e+07, -2.78676973e+09, 5.30223770e+08,
2.69016725e+09, -1.75853392e+09, -5.36809617e+08,
-3.23070948e+09, 3.30450457e+09, 2.31223857e+09,
1.34270089e+09, -6.87876720e+08, 2.82014777e+09,
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2.31878044e+09, 3.66091910e+08, -3.40642082e+09,
-1.76717584e+09, 1.74166052e+09, -2.04702245e+09,
4.94505988e+09, 5.28660222e+11, 7.01755659e+05,
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1.45549171e+02, 1.13605036e+03, 4.65697353e+03,
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1.43375622e+04, 8.92739806e+07, 7.35504854e+07,
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5.48098726e+00],
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5.55692116e+09, -4.39830814e+09, 5.45244668e+09,
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-1.55024480e+12]]))
B_nv = sp.Matrix(np.array([[-4.47125085e+08, -4.47125324e+08],
[ 1.38029089e+08, -1.38027354e+08],
[-1.15063079e+09, -1.15063045e+09],
[ 2.57457952e+08, -2.57459248e+08],
[-1.89536659e+09, -1.89536625e+09],
[ 3.42184448e+08, -3.42183487e+08],
[-2.30166395e+09, -2.30166430e+09],
[ 3.80748377e+08, -3.80750901e+08],
[-2.59394972e+09, -2.59395013e+09],
[ 3.67909713e+08, -3.67907331e+08],
[-2.42015873e+09, -2.42015876e+09],
[-3.05346944e+08, 3.05345252e+08],
[-2.03136135e+09, -2.03136117e+09],
[ 2.01480252e+08, -2.01477631e+08],
[-1.16109752e+09, -1.16109758e+09],
[ 7.03325014e+07, -7.03389051e+07],
[ 3.57152137e+02, 9.28673896e+02],
[-7.90044796e+01, -6.46596016e+01],
[ 6.59495413e+02, 3.53740734e+01],
[ 3.99548851e+01, 9.10003664e+01],
[-1.69015050e+02, -2.53940367e+02],
[ 9.88949719e+01, 1.82499568e+02],
[ 6.61293656e+02, 8.19002709e+02],
[-9.92896097e+01, -1.11864087e+02],
[ 6.45454990e+01, -8.49420741e+00],
[ 3.08153430e+02, 4.42567371e+02],
[ 1.26827594e+01, -6.69042570e+01],
[-1.39852412e+02, -3.58657641e+02],
[-6.70707766e+01, -1.93703428e+02],
[ 1.02886320e+01, -1.75124433e+01],
[-2.83096198e+02, -6.58092545e+02],
[-1.73688675e+01, 1.22361737e+01],
[-8.11256854e+01, -2.33060865e+02],
[-2.00094447e+02, -2.35882359e+02],
[-2.98589989e+02, -4.29229794e+02],
[-1.63101797e+02, -3.33941016e+02],
[-3.90197694e+01, -7.41741817e+01],
[ 6.47161349e+01, 1.62312179e+02],
[ 1.41760554e+01, 1.10566538e+01],
[ 3.14086384e+02, 3.28055417e+02],
[ 3.13030558e+02, 4.32019900e+02],
[-2.04003587e+01, -1.12645018e+02],
[ 9.81601147e+01, 2.31401803e+02],
[ 7.16653771e+02, 9.24775915e+02],
[-1.21857051e+03, -9.31434198e+02],
[ 3.06347907e+01, 1.12655697e+02],
[-4.38574918e+01, -6.88001340e+02],
[ 1.30686839e+02, 4.57645090e+02],
[ 6.55590394e+01, 7.41716191e+01],
[-1.46564310e+02, -2.56888953e+02],
[ 3.46083958e+02, 7.64143779e+02],
[ 2.22172115e+02, 5.30038685e+02],
[ 1.72700945e+02, 2.03947203e+02],
[ 2.45314321e+02, 5.26817475e+02],
[ 3.77302474e+01, 1.02876158e+02],
[-2.06434656e+02, -4.80501983e+02],
[-1.83044136e+02, -6.00946757e+02],
[-9.66821621e+01, -1.49494829e+02],
[-7.72264751e+01, -1.93299389e+02],
[ 1.05253816e+02, 1.64767140e+02],
[ 8.18144818e+01, 1.18012876e+02],
[ 2.26003558e+02, 3.85565420e+02],
[ 1.15297860e+02, -1.04542832e+02],
[ 3.45835307e+01, 8.97268767e+01],
[-1.89715369e+10, -1.89715369e+10],
[ 5.85652175e+09, -5.85652157e+09],
[-4.88209534e+10, -4.88209534e+10],
[ 1.09238633e+10, -1.09238632e+10],
[-8.04190981e+10, -8.04190981e+10],
[-1.45185361e+10, 1.45185360e+10],
[ 9.76567536e+10, 9.76567536e+10],
[ 1.61546122e+10, -1.61546122e+10],
[ 1.10056350e+11, 1.10056350e+11],
[-1.56095312e+10, 1.56095312e+10],
[ 1.02681130e+11, 1.02681130e+11],
[ 1.29549652e+10, -1.29549654e+10],
[ 8.61843598e+10, 8.61843598e+10],
[-8.54808388e+09, 8.54808393e+09],
[ 4.92612931e+10, 4.92612930e+10],
[-2.98408491e+09, 2.98408488e+09],
[-7.36644184e+01, -1.07429161e+02],
[ 2.06367567e+01, 2.36384828e+01],
[ 6.08783150e+01, 9.76632834e+01],
[-1.35990539e+02, -9.11440441e+01],
[ 1.66560461e+01, 3.54527685e+00],
[-1.03573750e+01, -1.72739244e+01],
[-5.33190139e+01, -6.41108686e+01],
[-3.23596321e+01, -5.32943551e+01],
[ 1.04378423e+01, -1.21622073e+01],
[-2.33676640e+01, 6.37820298e+00],
[-2.31127442e+00, -5.13469220e+00],
[ 8.31513226e+00, 2.37395662e+01],
[ 1.83885927e+01, 1.30794503e+01],
[ 2.54435795e+01, 4.91990198e+01],
[ 3.10779768e+01, 5.38429202e+01],
[-1.65235605e+01, 1.74881776e+01],
[ 5.36494731e+10, 5.36494730e+10],
[ 1.65616952e+10, -1.65616953e+10],
[-1.38062170e+11, -1.38062170e+11],
[ 3.08922327e+10, -3.08922326e+10],
[ 2.27424832e+11, 2.27424832e+11],
[ 4.10589656e+10, -4.10589657e+10],
[-2.76181498e+11, -2.76181498e+11],
[ 4.56873891e+10, -4.56873891e+10],
[ 3.11259448e+11, 3.11259448e+11],
[-4.41473668e+10, 4.41473667e+10],
[ 2.90410758e+11, 2.90410758e+11],
[ 3.66407883e+10, -3.66407883e+10],
[ 2.43760121e+11, 2.43760121e+11],
[-2.41772874e+10, 2.41772874e+10],
[ 1.39331081e+11, 1.39331081e+11],
[-8.44025303e+09, 8.44025294e+09],
[ 5.59497495e+00, 1.13523046e+01],
[ 4.09645370e+01, 1.86317656e+01],
[-2.52878329e+01, -3.27688187e+00],
[-8.84757420e+01, -8.16450524e+01],
[ 5.62406416e+00, 7.08481705e+00],
[-2.83494514e+00, 1.91716403e+01],
[ 4.73972406e+01, 5.23032185e+01],
[ 2.73639787e+01, 2.17160903e+00],
[ 6.28452954e+01, 4.99782079e+01],
[ 1.98639999e+00, -4.18047909e+00],
[-3.59788818e+00, -1.45421091e+01],
[ 3.22915192e+00, 2.03153930e+01],
[ 1.55575725e+01, 3.56954951e+01],
[-7.37305968e+00, 3.07320890e+01],
[ 2.70656581e+01, 9.01490453e+00],
[ 3.04565155e+01, 3.49007335e+01],
[ 1.96186939e+01, 2.80050383e+01],
[ 3.34460518e+01, 4.28965049e+01],
[ 4.63404881e+00, 3.10113402e+00],
[-1.94384497e+01, -1.86488538e+01],
[-1.23840237e+00, -4.29241701e-01],
[ 7.68426332e+01, 7.74902842e+01],
[-1.25039545e+01, -8.93882440e+00],
[-2.65031656e+01, -2.03369226e+01],
[ 2.08663082e+01, 4.96593141e+01],
[-4.64985373e+01, -9.96614924e+01],
[ 7.92847454e+00, -3.36514577e+01],
[ 4.26235910e+01, 1.88585718e+01],
[ 1.35125916e+01, 1.68836261e+00],
[ 5.93963236e+00, -2.75272325e+00],
[-2.05765464e+00, 7.20181698e+00],
[-2.05178581e+01, -9.44970801e+00],
[ 7.17552797e+00, 1.99482035e+01],
[-1.63620968e+01, -2.01367065e+01],
[ 2.64147741e+01, 1.84998916e+01],
[ 1.54517601e+01, 2.88894814e+01],
[-4.11756702e+01, -4.50005503e+01],
[ 3.67343662e+00, -6.81389156e-01],
[ 3.50061253e+01, 2.01661959e+01],
[ 2.46127029e+01, 4.57011158e+01],
[-4.78056999e+01, -6.16927356e+01],
[ 1.32846655e+01, 2.73373187e+01],
[ 1.06065116e+01, 1.16771974e+01],
[ 2.46771505e+01, 8.46408136e+00],
[-4.88353102e+01, -7.54539666e+01],
[ 5.89263859e+00, -2.32972126e+01],
[ 1.41630484e+02, 1.86276978e+02],
[ 6.67658029e+00, -2.00063443e+01],
[ 2.13181771e+12, 2.13181771e+12],
[ 6.61224360e+11, -6.61224359e+11],
[-5.55460242e+12, -5.55460242e+12],
[ 1.25568374e+12, -1.25568374e+12],
[-9.35845603e+12, -9.35845603e+12],
[ 1.71263076e+12, -1.71263076e+12],
[-1.16805561e+13, -1.16805561e+13],
[-1.95738787e+12, 1.95738787e+12],
[-1.34781826e+13, -1.34781826e+13],
[-1.92534143e+12, 1.92534143e+12],
[-1.26997005e+13, -1.26997005e+13],
[-1.59935591e+12, 1.59935591e+12],
[-1.05807110e+13, -1.05807110e+13],
[ 1.04142810e+12, -1.04142809e+12],
[-5.95609875e+12, -5.95609875e+12],
[ 3.58811877e+11, -3.58811876e+11],
[-8.70850669e+01, -2.98960766e+01],
[ 8.05897026e+01, 5.88031625e+01],
[-9.43489017e+01, -4.24096024e+01],
[ 4.04251055e+01, 5.07140452e+01],
[ 7.65107760e+01, 6.57970342e+01],
[-1.14165006e+02, -6.49510319e+01],
[-6.45574343e+01, -2.05209000e+01],
[-7.04207898e-02, 5.99564863e+00],
[ 1.15297721e+02, 5.68167992e+01],
[-1.45472056e+02, -8.76092439e+01],
[-7.50237289e+00, 5.60698974e+01],
[ 3.66600155e+02, 2.98460202e+02],
[ 1.05301027e+02, 6.99630510e+01],
[-3.18888077e+02, -2.61711330e+02],
[-3.20818047e+02, -2.66675879e+02],
[-1.25485500e+02, -5.99043500e+01],
[ 1.38934772e+12, 1.38934772e+12],
[-4.37596253e+11, 4.37596252e+11],
[ 3.77192038e+12, 3.77192038e+12],
[ 8.84312302e+11, -8.84312301e+11],
[-6.91055779e+12, -6.91055779e+12],
[-1.34110300e+12, 1.34110300e+12],
[ 9.81194936e+12, 9.81194936e+12],
[ 1.78425084e+12, -1.78425084e+12],
[-1.34795127e+13, -1.34795127e+13],
[-2.13321647e+12, 2.13321647e+12],
[-3.56292304e+12, -3.56292304e+12],
[ 1.57027989e+13, 1.57027989e+13],
[-1.11463288e+12, 1.11463287e+12],
[ 2.21444210e+12, -2.21444209e+12],
[ 9.50282105e+12, 9.50282104e+12],
[-1.63678385e+13, -1.63678385e+13],
[-2.19538675e+12, 2.19538675e+12],
[-1.78247657e+12, 1.78247656e+12],
[-1.68565325e+13, -1.68565324e+13],
[ 1.10694447e+13, 1.10694447e+13],
[-7.04088902e+11, 7.04088901e+11],
[-2.76422256e+01, -8.97150214e+01],
[ 2.00242556e+02, 1.83942561e+02],
[-2.43720658e+01, -1.27284757e+02],
[-1.19369197e+02, -8.29171372e+01],
[ 3.66950215e+01, -1.88624376e+01],
[-8.13632810e+01, -7.71950021e+01],
[ 8.08085482e+01, 6.01128331e+01],
[-3.96630761e+00, 7.81782965e+01],
[-2.19871385e+01, 3.52124438e+01],
[ 1.68585052e+02, 2.34455832e+02],
[-1.55993077e+02, -9.29149903e+01],
[-1.56815149e+01, -4.63665495e+01],
[-2.02583556e+01, 4.76340273e+01],
[-1.11213714e+02, -8.78733468e+01],
[-6.89730762e+01, -5.69616896e+01],
[-1.66166129e+02, -1.46237003e+02],
[-3.20882121e+12, 3.20882120e+12],
[ 2.30336838e+13, 2.30336838e+13],
[-4.12177913e+12, 4.12177912e+12],
[ 3.08558228e+13, 3.08558228e+13],
[ 4.89952687e+12, -4.89952687e+12],
[-3.69254509e+13, -3.69254509e+13],
[ 5.50017284e+12, -5.50017283e+12],
[ 4.50435419e+13, 4.50435419e+13],
[ 1.29520492e+12, 1.29520492e+12],
[-4.09200097e+11, 4.09200096e+11],
[-3.54658893e+12, -3.54658893e+12],
[-8.38605510e+11, 8.38605512e+11],
[-6.63601365e+12, -6.63601364e+12],
[ 5.86680467e+12, -5.86680466e+12],
[ 1.31119253e+12, -1.31119253e+12],
[-9.84125820e+12, -9.84125820e+12],
[ 1.85530131e+12, -1.85530130e+12],
[ 1.47452455e+13, 1.47452455e+13],
[ 2.50493932e+12, -2.50493931e+12],
[ 2.03471709e+13, 2.03471709e+13],
[ 3.28779935e+12, -3.28779934e+12],
[-2.93414962e+13, -2.93414962e+13],
[-4.16735249e+12, 4.16735247e+12],
[-4.99650082e+13, -4.99650082e+13],
[ 3.83960040e+13, 3.83960040e+13],
[ 4.80840176e+12, -4.80840176e+12],
[-6.02842164e+12, 6.02842163e+12]]))
B1_nv = sp.Matrix(np.array([[-4.47125085e+08, -4.47125324e+08],
[ 1.38029089e+08, -1.38027354e+08],
[-1.15063079e+09, -1.15063045e+09],
[ 2.57457952e+08, -2.57459248e+08],
[-1.89536659e+09, -1.89536625e+09],
[ 3.42184448e+08, -3.42183487e+08],
[-2.30166395e+09, -2.30166430e+09],
[ 3.80748377e+08, -3.80750901e+08],
[-2.59394972e+09, -2.59395013e+09],
[ 3.67909713e+08, -3.67907331e+08],
[-2.42015873e+09, -2.42015876e+09],
[-3.05346944e+08, 3.05345252e+08],
[-2.03136135e+09, -2.03136117e+09],
[ 2.01480252e+08, -2.01477631e+08],
[-1.16109752e+09, -1.16109758e+09],
[ 7.03325014e+07, -7.03389051e+07],
[ 3.57152137e+02, 9.28673896e+02],
[-7.90044796e+01, -6.46596016e+01],
[ 6.59495413e+02, 3.53740734e+01],
[ 3.99548851e+01, 9.10003664e+01],
[-1.69015050e+02, -2.53940367e+02],
[ 9.88949719e+01, 1.82499568e+02],
[ 6.61293656e+02, 8.19002709e+02],
[-9.92896097e+01, -1.11864087e+02],
[ 6.45454990e+01, -8.49420741e+00],
[ 3.08153430e+02, 4.42567371e+02],
[ 1.26827594e+01, -6.69042570e+01],
[-1.39852412e+02, -3.58657641e+02],
[-6.70707766e+01, -1.93703428e+02],
[ 1.02886320e+01, -1.75124433e+01],
[-2.83096198e+02, -6.58092545e+02],
[-1.73688675e+01, 1.22361737e+01],
[-8.11256854e+01, -2.33060865e+02],
[-2.00094447e+02, -2.35882359e+02],
[-2.98589989e+02, -4.29229794e+02],
[-1.63101797e+02, -3.33941016e+02],
[-3.90197694e+01, -7.41741817e+01],
[ 6.47161349e+01, 1.62312179e+02],
[ 1.41760554e+01, 1.10566538e+01],
[ 3.14086384e+02, 3.28055417e+02],
[ 3.13030558e+02, 4.32019900e+02],
[-2.04003587e+01, -1.12645018e+02],
[ 9.81601147e+01, 2.31401803e+02],
[ 7.16653771e+02, 9.24775915e+02],
[-1.21857051e+03, -9.31434198e+02],
[ 3.06347907e+01, 1.12655697e+02],
[-4.38574918e+01, -6.88001340e+02],
[ 1.30686839e+02, 4.57645090e+02],
[ 6.55590394e+01, 7.41716191e+01],
[-1.46564310e+02, -2.56888953e+02],
[ 3.46083958e+02, 7.64143779e+02],
[ 2.22172115e+02, 5.30038685e+02],
[ 1.72700945e+02, 2.03947203e+02],
[ 2.45314321e+02, 5.26817475e+02],
[ 3.77302474e+01, 1.02876158e+02],
[-2.06434656e+02, -4.80501983e+02],
[-1.83044136e+02, -6.00946757e+02],
[-9.66821621e+01, -1.49494829e+02],
[-7.72264751e+01, -1.93299389e+02],
[ 1.05253816e+02, 1.64767140e+02],
[ 8.18144818e+01, 1.18012876e+02],
[ 2.26003558e+02, 3.85565420e+02],
[ 1.15297860e+02, -1.04542832e+02],
[ 3.45835307e+01, 8.97268767e+01],
[-1.89715369e+10, -1.89715369e+10],
[ 5.85652175e+09, -5.85652157e+09],
[-4.88209534e+10, -4.88209534e+10],
[ 1.09238633e+10, -1.09238632e+10],
[-8.04190981e+10, -8.04190981e+10],
[-1.45185361e+10, 1.45185360e+10],
[ 9.76567536e+10, 9.76567536e+10],
[ 1.61546122e+10, -1.61546122e+10],
[ 1.10056350e+11, 1.10056350e+11],
[-1.56095312e+10, 1.56095312e+10],
[ 1.02681130e+11, 1.02681130e+11],
[ 1.29549652e+10, -1.29549654e+10],
[ 8.61843598e+10, 8.61843598e+10],
[-8.54808388e+09, 8.54808393e+09],
[ 4.92612931e+10, 4.92612930e+10],
[-2.98408491e+09, 2.98408488e+09],
[-7.36644184e+01, -1.07429161e+02],
[ 2.06367567e+01, 2.36384828e+01],
[ 6.08783150e+01, 9.76632834e+01],
[-1.35990539e+02, -9.11440441e+01],
[ 1.66560461e+01, 3.54527685e+00],
[-1.03573750e+01, -1.72739244e+01],
[-5.33190139e+01, -6.41108686e+01],
[-3.23596321e+01, -5.32943551e+01],
[ 1.04378423e+01, -1.21622073e+01],
[-2.33676640e+01, 6.37820298e+00],
[-2.31127442e+00, -5.13469220e+00],
[ 8.31513226e+00, 2.37395662e+01],
[ 1.83885927e+01, 1.30794503e+01],
[ 2.54435795e+01, 4.91990198e+01],
[ 3.10779768e+01, 5.38429202e+01],
[-1.65235605e+01, 1.74881776e+01],
[ 5.36494731e+10, 5.36494730e+10],
[ 1.65616952e+10, -1.65616953e+10],
[-1.38062170e+11, -1.38062170e+11],
[ 3.08922327e+10, -3.08922326e+10],
[ 2.27424832e+11, 2.27424832e+11],
[ 4.10589656e+10, -4.10589657e+10],
[-2.76181498e+11, -2.76181498e+11],
[ 4.56873891e+10, -4.56873891e+10],
[ 3.11259448e+11, 3.11259448e+11],
[-4.41473668e+10, 4.41473667e+10],
[ 2.90410758e+11, 2.90410758e+11],
[ 3.66407883e+10, -3.66407883e+10],
[ 2.43760121e+11, 2.43760121e+11],
[-2.41772874e+10, 2.41772874e+10],
[ 1.39331081e+11, 1.39331081e+11],
[-8.44025303e+09, 8.44025294e+09],
[ 5.59497495e+00, 1.13523046e+01],
[ 4.09645370e+01, 1.86317656e+01],
[-2.52878329e+01, -3.27688187e+00],
[-8.84757420e+01, -8.16450524e+01],
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C1_nv = sp.Matrix(np.array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
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D12_nv = sp.Matrix(np.array([[0., 0.],
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D21_nv = sp.Matrix(np.array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
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# ---------- 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 = []