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Details for: "Plate Experiment for the active vibration damping of large flexible space structures, example of order 10"

Name: Plate Experiment for the active vibration damping of large flexible space structures, example of order 10 (Key: CO153)
Path: ackrep_data/system_models/compleib_models/DLR2 View on GitHub
Type: system_model
Short Description: DLR2 like DLR1, original system .mat file generated by /export/home/leibfr/tankred/work/DLR_40_data.m on msun10
Created: 2022-10-10 15:57:36
Compatible Environment: default_conda_environment (Key: CDAMA)
Source Code [ / ] simulation.py
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:57:37).

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([-1.30536565e+00,  9.39559776e-02, -4.05886861e-01, -4.19803171e-01,
       -4.96150118e-01, -6.00312256e-02,  2.11699878e-01,  2.34455256e-02,
        8.77194491e-02, -4.92084356e-02, -1.25297647e-02, -8.98890907e-04,
        1.50758410e-02,  3.60165239e-03, -6.64936291e-03, -5.28956453e-03,
        2.37386301e-03, -1.32426115e-03,  7.52496957e-04, -1.06850011e-03,
       -3.44821749e-01, -1.64767066e+00,  3.35899154e+00,  4.24962056e+00,
       -1.61270602e+00,  6.77158086e+00,  1.96089152e+00,  5.22622896e+00,
        6.97539726e-01, -3.29191603e+00,  3.21114854e+00,  2.12398548e+00,
       -1.21695592e+00, -8.66723707e-01,  2.38077276e-01, -2.97369689e-01,
        1.78032734e-01,  1.32692003e-01, -1.69427780e-01, -1.21475772e-01])

    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 15:57:37).

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 = 40

        # 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 15:57:37).

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 = 'Plate Experiment for the active vibration damping of large flexible space structures, example of order 10'


# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 40, 40)
B = sp.MatrixSymbol('B', 40, 2)
B1 = sp.MatrixSymbol('B1', 40, 1)
C1 = sp.MatrixSymbol('C1', 42, 40)
C = sp.MatrixSymbol('C', 2, 40)
D11 = sp.MatrixSymbol('D11', 42, 1)
D12 = sp.MatrixSymbol('D12', 42, 2)
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,  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,
         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,
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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,
         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,
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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,
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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],
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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,
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         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,
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        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -1.84158470e+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, -1.35705000e+00,
        -0.00000000e+00],
       [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -1.89670738e+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,
        -1.37721000e+00]]))
B_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.        ],
       [ 0.        ,  0.        ],
       [ 0.        ,  0.        ],
       [ 0.        ,  0.        ],
       [ 0.        ,  0.        ],
       [ 0.0674561 , -0.0674559 ],
       [ 0.0936079 ,  0.093608  ],
       [ 0.143665  ,  0.143665  ],
       [ 0.0808331 , -0.0808331 ],
       [-0.0707422 , -0.0707422 ],
       [-0.0309156 ,  0.0309156 ],
       [ 0.060544  ,  0.060544  ],
       [ 0.00277099,  0.00277099],
       [ 0.040953  , -0.040953  ],
       [-0.118247  , -0.118247  ],
       [-0.149486  , -0.149486  ],
       [-0.080104  , -0.080104  ],
       [ 0.0849413 , -0.0849413 ],
       [ 0.158145  ,  0.158145  ],
       [ 0.0199461 ,  0.0199461 ],
       [ 0.0528277 , -0.0528276 ],
       [ 0.0342809 , -0.0342809 ],
       [ 0.138786  ,  0.138786  ],
       [ 0.275623  , -0.275623  ],
       [-0.0635756 , -0.0635756 ]]))
B1_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.        ],
       [ 0.        ,  0.        ],
       [ 0.        ,  0.        ],
       [ 0.        ,  0.        ],
       [ 0.        ,  0.        ],
       [ 0.0674561 , -0.0674559 ],
       [ 0.0936079 ,  0.093608  ],
       [ 0.143665  ,  0.143665  ],
       [ 0.0808331 , -0.0808331 ],
       [-0.0707422 , -0.0707422 ],
       [-0.0309156 ,  0.0309156 ],
       [ 0.060544  ,  0.060544  ],
       [ 0.00277099,  0.00277099],
       [ 0.040953  , -0.040953  ],
       [-0.118247  , -0.118247  ],
       [-0.149486  , -0.149486  ],
       [-0.080104  , -0.080104  ],
       [ 0.0849413 , -0.0849413 ],
       [ 0.158145  ,  0.158145  ],
       [ 0.0199461 ,  0.0199461 ],
       [ 0.0528277 , -0.0528276 ],
       [ 0.0342809 , -0.0342809 ],
       [ 0.138786  ,  0.138786  ],
       [ 0.275623  , -0.275623  ],
       [-0.0635756 , -0.0635756 ]]))
C1_nv = sp.Matrix(np.array([[3162.27766017,    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.        , 3162.27766017,    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.        , 3162.27766017,    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.        , 3162.27766017,
           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.        ,
        1000.        ,    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.        , 1000.        ,    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.        , 1000.        ,    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.        , 1000.        ,
           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.        ,
        3162.27766017,    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.        , 3162.27766017,    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.        , 3162.27766017,    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.        , 3162.27766017,
           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.        ,
        1000.        ,    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.        , 1000.        ,    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.        , 1000.        ,    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.        , 1000.        ,
           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.        ,
         707.10678119,    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.        ,  707.10678119,    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.        ,  707.10678119,    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.        ,  707.10678119,
           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.        ,
         316.22776602,    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.        ,  316.22776602,    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.        ,  316.22776602,    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.        ,  316.22776602,
           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.        ,
         707.10678119,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
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       [   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.        ,  707.10678119,    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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           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,  707.10678119,    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.        ,  707.10678119,
           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.        ,
         316.22776602,    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.        ,  316.22776602,    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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           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ],
       [   0.        ,    0.        ,    0.        ,    0.        ,
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       [   0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
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         316.22776602,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ],
       [   0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,  316.22776602,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ],
       [   0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,  316.22776602,
           0.        ,    0.        ,    0.        ,    0.        ],
       [   0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
         316.22776602,    0.        ,    0.        ,    0.        ],
       [   0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,  316.22776602,    0.        ,    0.        ],
       [   0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,  316.22776602,    0.        ],
       [   0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
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           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,    0.        ,
           0.        ,    0.        ,    0.        ,  316.22776602],
       [   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.        ]]))
C_nv = sp.Matrix(np.array([[-2.74346e-01,  2.56495e-07,  1.24771e-08,  6.38627e-02,
        -9.02473e-09, -3.54791e-01,  5.15609e-09,  9.47967e-09,
         2.89055e-01,  7.72417e-08, -1.09564e-08, -1.49674e-09,
         2.04444e-01,  2.42373e-08, -6.97884e-08, -3.89486e-01,
        -9.25547e-02,  1.85888e-07, -5.84968e-01, -1.94107e-07,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00],
       [-2.01214e-08, -3.02832e-02,  1.75384e-01,  2.02140e-08,
         8.07153e-02,  1.12285e-08,  3.35051e-01, -8.01912e-02,
         1.20779e-07, -2.82554e-01,  5.26414e-01,  3.23432e-01,
        -1.96047e-09,  8.75089e-02, -5.02781e-01,  1.28096e-07,
         2.59987e-09, -7.11243e-01,  1.06339e-07, -1.21232e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00,
         0.00000e+00,  0.00000e+00,  0.00000e+00,  0.00000e+00]]))
D11_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.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.]]))
D12_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.      ],
       [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.      ],
       [0.083666, 0.      ],
       [0.      , 0.083666]]))
D21_nv = sp.Matrix(np.array([[0.],
       [0.]]))


# ---------- 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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