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Details for: "Perturbetd linear cable mass problem of order 20"

Name: Perturbetd linear cable mass problem of order 20 (Key: CO145)
Path: ackrep_data/system_models/compleib_models/CM2_IS View on GitHub
Type: system_model
Short Description: CM2_IS To CM1_IS corresponding example of order 60, sd=9.5825e-003
Created: 2022-10-10 15:55:37
Compatible Environment: default_conda_environment (Key: CDAMA)
Source Code [ / ] simulation.py
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:55:38).

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.array([ 0.01207624, -0.13492355, -0.32936458, -0.46610571, -0.42398212,
       -0.39047412, -0.56846631, -0.80994763, -0.97399933, -0.90045424,
       -0.85526318, -0.99698742, -1.20322352, -1.38010833, -1.48848783,
       -1.59109267, -1.63703334, -1.55743944, -1.61551417, -1.8445741 ,
       -2.11981326, -2.32554924, -2.47334724, -2.65201334, -2.64891969,
       -2.48236355, -2.46672362, -2.44719116, -2.21099356, -2.23449385,
       -2.04258435, -1.27996361,  1.58089398,  2.0390397 ,  0.62695446,
       -0.98099636, -0.04267307,  0.47500218,  0.92127981,  1.15181121,
        2.21564633,  2.12998222, -1.44585034, -1.14112192,  0.50499958,
        4.32230072,  3.37499646,  0.793958  ,  2.23085092,  0.45587773,
       -1.17997268, -0.6813359 ,  1.81535603,  3.39961798,  3.06844998,
        3.89660687,  4.59208669,  2.73809837,  0.88755631, -0.14420534])

    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 15:55:38).

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 = 1

        # Set "sys_dim" to constant value, if system dimension is constant 
        self.sys_dim = 60

        # 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(1) # 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 15:55:38).

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 = 'Perturbetd linear cable mass problem of order 20'


# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 60, 60)
B = sp.MatrixSymbol('B', 60, 1)
B1 = sp.MatrixSymbol('B1', 60, 1)
C1 = sp.MatrixSymbol('C1', 3, 60)
C = sp.MatrixSymbol('C', 2, 60)
D11 = sp.MatrixSymbol('D11', 3, 1)
D12 = sp.MatrixSymbol('D12', 3, 1)
D21 = sp.MatrixSymbol('D21', 2, 1)

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([[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         1.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  1.00000000e+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,  1.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  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,
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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,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
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         6.16142517e-06, -2.29947520e-05,  8.58175828e-05,
        -3.20275579e-04,  1.19528473e-03, -4.46086336e-03,
         1.66481687e-02, -6.21318114e-02,  2.31879077e-01,
        -8.65384496e-01,  3.22965891e+00, -1.20532511e+01,
         4.49833456e+01, -1.67880131e+02,  6.26537180e+02,
        -9.88268589e+02,  6.26537174e+02, -1.67880109e+02,
         4.49832620e+01, -1.20529390e+01,  3.22849391e+00,
        -8.61036649e-01,  2.15652689e-01, -3.62046410e-02,
         1.05830044e-13, -4.23320176e-13,  1.58745066e-12,
        -5.92648247e-12,  2.21184792e-11, -8.25474344e-11,
         3.08071258e-10, -1.14973760e-09,  4.29087914e-09,
        -1.60137790e-08,  5.97642367e-08, -2.23043168e-07,
         8.32408434e-07, -3.10659057e-06,  1.15939538e-05,
        -4.32692248e-05,  1.61482945e-04, -6.02662557e-04,
         2.24916728e-03, -8.39400657e-03,  3.13268590e-02,
        -3.98309294e-02,  3.13268587e-02, -8.39400546e-03,
         2.24916310e-03, -6.02646949e-04,  1.61424695e-04,
        -4.30518325e-05,  1.07826345e-05, -1.81022330e-06],
       [-5.67141492e-10,  2.26856597e-09, -8.50712238e-09,
         3.17599236e-08, -1.18532572e-07,  4.42370364e-07,
        -1.65094888e-06,  6.16142517e-06, -2.29947518e-05,
         8.58175820e-05, -3.20275576e-04,  1.19528472e-03,
        -4.46086332e-03,  1.66481685e-02, -6.21318108e-02,
         2.31879075e-01, -8.65384489e-01,  3.22965888e+00,
        -1.20532510e+01,  4.49833452e+01, -1.67880130e+02,
         6.26537174e+02, -9.88268568e+02,  6.26537097e+02,
        -1.67879819e+02,  4.49821807e+01, -1.20489033e+01,
         3.21343252e+00, -8.04826793e-01,  1.35117560e-01,
        -2.83570746e-14,  1.13428298e-13, -4.25356119e-13,
         1.58799618e-12, -5.92662859e-12,  2.21185182e-11,
        -8.25474442e-11,  3.08071259e-10, -1.14973759e-09,
         4.29087910e-09, -1.60137788e-08,  5.97642362e-08,
        -2.23043166e-07,  8.32408427e-07, -3.10659054e-06,
         1.15939537e-05, -4.32692244e-05,  1.61482944e-04,
        -6.02662551e-04,  2.24916726e-03, -8.39400650e-03,
         3.13268587e-02, -3.98309284e-02,  3.13268548e-02,
        -8.39399097e-03,  2.24910903e-03, -6.02445165e-04,
         1.60671626e-04, -4.02413396e-05,  6.75584534e-06],
       [ 1.51965086e-10, -6.07860344e-10,  2.27947629e-09,
        -8.51004481e-09,  3.17607030e-08, -1.18532767e-07,
         4.42370365e-07, -1.65094869e-06,  6.16142441e-06,
        -2.29947489e-05,  8.58175714e-05, -3.20275537e-04,
         1.19528457e-03, -4.46086276e-03,  1.66481665e-02,
        -6.21318031e-02,  2.31879046e-01, -8.65384381e-01,
         3.22965848e+00, -1.20532495e+01,  4.49833397e+01,
        -1.67880109e+02,  6.26537097e+02, -9.88268278e+02,
         6.26536015e+02, -1.67875784e+02,  4.49671193e+01,
        -1.19926934e+01,  3.00365448e+00, -5.04265597e-01,
         7.59825430e-15, -3.03930172e-14,  1.13973814e-13,
        -4.25502241e-13,  1.58803515e-12, -5.92663835e-12,
         2.21185183e-11, -8.25474347e-11,  3.08071221e-10,
        -1.14973745e-09,  4.29087857e-09, -1.60137768e-08,
         5.97642287e-08, -2.23043138e-07,  8.32408324e-07,
        -3.10659016e-06,  1.15939523e-05, -4.32692191e-05,
         1.61482924e-04, -6.02662477e-04,  2.24916698e-03,
        -8.39400546e-03,  3.13268548e-02, -3.98309139e-02,
         3.13268008e-02, -8.39378918e-03,  2.24835596e-03,
        -5.99634672e-04,  1.50182724e-04, -2.52131581e-05],
       [-4.07188518e-11,  1.62875407e-10, -6.10782777e-10,
         2.28025570e-09, -8.51024002e-09,  3.17607044e-08,
        -1.18532578e-07,  4.42369606e-07, -1.65094585e-06,
         6.16141378e-06, -2.29947093e-05,  8.58174233e-05,
        -3.20274984e-04,  1.19528251e-03, -4.46085506e-03,
         1.66481377e-02, -6.21316959e-02,  2.31878646e-01,
        -8.65382888e-01,  3.22965291e+00, -1.20532287e+01,
         4.49832620e+01, -1.67879819e+02,  6.26536015e+02,
        -9.88264242e+02,  6.26520954e+02, -1.67819574e+02,
         4.47573412e+01, -1.12097911e+01,  1.88194483e+00,
        -2.03594259e-15,  8.14377036e-15, -3.05391388e-14,
         1.14012785e-13, -4.25512001e-13,  1.58803522e-12,
        -5.92662888e-12,  2.21184803e-11, -8.25472923e-11,
         3.08070689e-10, -1.14973546e-09,  4.29087116e-09,
        -1.60137492e-08,  5.97641256e-08, -2.23042753e-07,
         8.32406887e-07, -3.10658480e-06,  1.15939323e-05,
        -4.32691444e-05,  1.61482645e-04, -6.02661437e-04,
         2.24916310e-03, -8.39399097e-03,  3.13268008e-02,
        -3.98307121e-02,  3.13260477e-02, -8.39097869e-03,
         2.23786706e-03, -5.60489557e-04,  9.40967869e-05],
       [ 1.09103212e-11, -4.36412847e-11,  1.63654818e-10,
        -6.10977986e-10,  2.28025712e-09, -8.51005051e-09,
         3.17599449e-08, -1.18529729e-07,  4.42358972e-07,
        -1.65090616e-06,  6.16126566e-06, -2.29941565e-05,
         8.58153603e-05, -3.20267285e-04,  1.19525378e-03,
        -4.46074783e-03,  1.66477375e-02, -6.21302023e-02,
         2.31873072e-01, -8.65362085e-01,  3.22957527e+00,
        -1.20529390e+01,  4.49821807e+01, -1.67875784e+02,
         6.26520954e+02, -9.88208033e+02,  6.26311176e+02,
        -1.67036672e+02,  4.18355101e+01, -7.02351372e+00,
         5.45516059e-16, -2.18206423e-15,  8.18274088e-15,
        -3.05488993e-14,  1.14012856e-13, -4.25502526e-13,
         1.58799725e-12, -5.92648646e-12,  2.21179486e-11,
        -8.25453079e-11,  3.08063283e-10, -1.14970782e-09,
         4.29076801e-09, -1.60133642e-08,  5.97626889e-08,
        -2.23037391e-07,  8.32386877e-07, -3.10651012e-06,
         1.15936536e-05, -4.32681042e-05,  1.61478763e-04,
        -6.02646949e-04,  2.24910903e-03, -8.39378918e-03,
         3.13260477e-02, -3.98279016e-02,  3.13155588e-02,
        -8.35183358e-03,  2.09177550e-03, -3.51173989e-04],
       [-2.92243290e-12,  1.16897316e-11, -4.38364935e-11,
         1.63656242e-10, -6.10788476e-10,  2.27949766e-09,
        -8.50720217e-09,  3.17493110e-08, -1.18490042e-07,
         4.42210857e-07, -1.65035339e-06,  6.15920268e-06,
        -2.29864574e-05,  8.57866267e-05, -3.20160050e-04,
         1.19485357e-03, -4.45925424e-03,  1.66421634e-02,
        -6.21093993e-02,  2.31795434e-01, -8.65072335e-01,
         3.22849391e+00, -1.20489033e+01,  4.49671193e+01,
        -1.67819574e+02,  6.26311176e+02, -9.87425130e+02,
         6.23389345e+02, -1.56132249e+02,  2.62121100e+01,
        -1.46121645e-16,  5.84486580e-16, -2.19182468e-15,
         8.18281212e-15, -3.05394238e-14,  1.13974883e-13,
        -4.25360109e-13,  1.58746555e-12, -5.92450210e-12,
         2.21105428e-11, -8.25176693e-11,  3.07960134e-10,
        -1.14932287e-09,  4.28933134e-09, -1.60080025e-08,
         5.97426786e-08, -2.22962712e-07,  8.32108169e-07,
        -3.10546996e-06,  1.15897717e-05, -4.32536168e-05,
         1.61424695e-04, -6.02445165e-04,  2.24835596e-03,
        -8.39097869e-03,  3.13155588e-02, -3.97887565e-02,
         3.11694672e-02, -7.80661245e-03,  1.31059917e-03],
       [ 7.79410432e-13, -3.11764173e-12,  1.16911565e-11,
        -4.36469842e-11,  1.62896780e-10, -6.07940137e-10,
         2.26886377e-09, -8.46751494e-09,  3.16011960e-08,
        -1.17937269e-07,  4.40147880e-07, -1.64265425e-06,
         6.13046912e-06, -2.28792222e-05,  8.53864199e-05,
        -3.18666457e-04,  1.18927941e-03, -4.43845118e-03,
         1.65645253e-02, -6.18196500e-02,  2.30714075e-01,
        -8.61036649e-01,  3.21343252e+00, -1.19926934e+01,
         4.47573412e+01, -1.67036672e+02,  6.23389345e+02,
        -9.76520708e+02,  5.82693486e+02, -9.78249265e+01,
         3.89705216e-17, -1.55882086e-16,  5.84557824e-16,
        -2.18234921e-15,  8.14483902e-15, -3.03970069e-14,
         1.13443188e-13, -4.23375747e-13,  1.58005980e-12,
        -5.89686345e-12,  2.20073940e-11, -8.21327125e-11,
         3.06523456e-10, -1.14396111e-09,  4.26932099e-09,
        -1.59333229e-08,  5.94639704e-08, -2.21922559e-07,
         8.28226265e-07, -3.09098250e-06,  1.15357037e-05,
        -4.30518325e-05,  1.60671626e-04, -5.99634672e-04,
         2.23786706e-03, -8.35183358e-03,  3.11694672e-02,
        -3.92435354e-02,  2.91346743e-02, -4.89122269e-03],
       [-1.95208829e-13,  7.80835314e-13, -2.92813243e-12,
         1.09316944e-11, -4.07986452e-11,  1.52262886e-10,
        -5.68252900e-10,  2.12074871e-09, -7.91474196e-09,
         2.95382191e-08, -1.10238134e-07,  4.11414319e-07,
        -1.53541914e-06,  5.73026224e-06, -2.13856298e-05,
         7.98122571e-05, -2.97863399e-04,  1.11164134e-03,
        -4.14870195e-03,  1.54831665e-02, -5.77839639e-02,
         2.15652689e-01, -8.04826793e-01,  3.00365448e+00,
        -1.12097911e+01,  4.18355101e+01, -1.56132249e+02,
         5.82693486e+02, -8.24641696e+02,  3.65087596e+02,
        -9.76044143e-18,  3.90417657e-17, -1.46406621e-16,
         5.46584720e-16, -2.03993226e-15,  7.61314431e-15,
        -2.84126450e-14,  1.06037436e-13, -3.95737098e-13,
         1.47691096e-12, -5.51190672e-12,  2.05707159e-11,
        -7.67709570e-11,  2.86513112e-10, -1.06928149e-09,
         3.99061285e-09, -1.48931699e-08,  5.55820669e-08,
        -2.07435097e-07,  7.74158323e-07, -2.88919819e-06,
         1.07826345e-05, -4.02413396e-05,  1.50182724e-04,
        -5.60489557e-04,  2.09177550e-03, -7.80661245e-03,
         2.91346743e-02, -3.16495848e-02,  1.82542916e-02],
       [ 1.42488196e-15, -5.69952784e-15,  2.13732294e-14,
        -7.97933898e-14,  2.97800330e-13, -1.11140793e-12,
         4.14783139e-12, -1.54799176e-11,  5.77718391e-11,
        -2.15607439e-10,  8.04657916e-10, -3.00302422e-09,
         1.12074390e-08, -4.18267317e-08,  1.56099488e-07,
        -5.82571220e-07,  2.17418539e-06, -8.11417034e-06,
         3.02824960e-05, -1.13015814e-04,  4.21780758e-04,
        -1.57410722e-03,  5.87464812e-03, -2.19244853e-02,
         8.18232929e-02, -3.05368686e-01,  1.13965145e+00,
        -4.25323713e+00,  1.58732970e+01, -1.25254569e+01,
         7.12440980e-20, -2.84976392e-19,  1.06866147e-18,
        -3.98966949e-18,  1.48900165e-17, -5.55703965e-17,
         2.07391569e-16, -7.73995881e-16,  2.88859195e-15,
        -1.07803719e-14,  4.02328958e-14, -1.50151211e-13,
         5.60371949e-13, -2.09133659e-12,  7.80497439e-12,
        -2.91285610e-11,  1.08709270e-10, -4.05708517e-10,
         1.51412480e-09, -5.65079068e-09,  2.10890379e-08,
        -7.87053610e-08,  2.93732406e-07, -1.09622426e-06,
         4.09116465e-06, -1.52684343e-05,  5.69825727e-05,
        -2.12661856e-04,  7.93664852e-04,  8.95655627e-03]]))
B_nv = sp.Matrix(np.array([[ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [-2.37480327e-17],
       [ 9.49921307e-17],
       [-3.56220490e-16],
       [ 1.32988983e-15],
       [-4.96333883e-15],
       [ 1.85234655e-14],
       [-6.91305231e-14],
       [ 2.57998627e-13],
       [-9.62863985e-13],
       [ 3.59345731e-12],
       [-1.34109653e-11],
       [ 5.00504037e-11],
       [-1.86790650e-10],
       [ 6.97112195e-10],
       [-2.60165813e-09],
       [ 9.70952033e-09],
       [-3.62364232e-08],
       [ 1.35236172e-07],
       [-5.04708266e-07],
       [ 1.88359689e-06],
       [-7.02967931e-06],
       [ 2.62351203e-05],
       [-9.79108020e-05],
       [ 3.65408088e-04],
       [-1.36372155e-03],
       [ 5.08947811e-03],
       [-1.89941909e-02],
       [ 7.08872854e-02],
       [-2.64554951e-01],
       [ 9.87332518e-01]]))
B1_nv = sp.Matrix(np.array([[ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [-2.37480327e-17],
       [ 9.49921307e-17],
       [-3.56220490e-16],
       [ 1.32988983e-15],
       [-4.96333883e-15],
       [ 1.85234655e-14],
       [-6.91305231e-14],
       [ 2.57998627e-13],
       [-9.62863985e-13],
       [ 3.59345731e-12],
       [-1.34109653e-11],
       [ 5.00504037e-11],
       [-1.86790650e-10],
       [ 6.97112195e-10],
       [-2.60165813e-09],
       [ 9.70952033e-09],
       [-3.62364232e-08],
       [ 1.35236172e-07],
       [-5.04708266e-07],
       [ 1.88359689e-06],
       [-7.02967931e-06],
       [ 2.62351203e-05],
       [-9.79108020e-05],
       [ 3.65408088e-04],
       [-1.36372155e-03],
       [ 5.08947811e-03],
       [-1.89941909e-02],
       [ 7.08872854e-02],
       [-2.64554951e-01],
       [ 9.87332518e-01]]))
C1_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., 1., 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., 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., 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., 1.],
       [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.,
        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.]]))
C_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., 1., 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., 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., 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., 1.]]))
D11_nv = sp.Matrix(np.array([[0.],
       [0.],
       [0.]]))
D12_nv = sp.Matrix(np.array([[0.        ],
       [0.        ],
       [1.22474487]]))
D21_nv = sp.Matrix(np.array([[0.],
       [1.]]))


# ---------- 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 = []

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