Automatic Control Knowledge Repository

# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:57:46).

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 = 3
    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(270)

    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

# This file was autogenerated from the template: system_model.py.template (2022-10-10 15:57:46).

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 = 3

        # Set "sys_dim" to constant value, if system dimension is constant 
        self.sys_dim = 270

        # 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
    

# This file was autogenerated from the template: parameters.py.template (2022-10-10 15:57:46).

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 = 'International Space Station SLICOT Working note 2002-2'


# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 270, 270)
B = sp.MatrixSymbol('B', 270, 3)
B1 = sp.MatrixSymbol('B1', 270, 1)
C1 = sp.MatrixSymbol('C1', 273, 270)
C = sp.MatrixSymbol('C', 3, 270)
D11 = sp.MatrixSymbol('D11', 273, 1)
D12 = sp.MatrixSymbol('D12', 273, 3)
D21 = sp.MatrixSymbol('D21', 3, 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,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  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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         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,
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         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00, -6.13398680e-01]]))
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],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 7.07573879e-07,  1.41283728e-01,  6.53919496e-06],
       [-5.06620672e-01, -1.19383139e-04, -3.62765895e-02],
       [-1.17894505e-10, -7.42090778e-10, -1.93602816e-11],
       [-8.14819266e-06, -1.10515849e-02, -1.72126665e-06],
       [-2.83747070e-06, -1.79995424e-02, -3.91652814e-06],
       [-4.38729147e-01, -9.62770869e-05, -3.00230737e-02],
       [ 3.64946244e-02,  2.39596452e-05,  7.94026055e-02],
       [ 6.56409965e-06, -1.61562545e-03,  4.60557000e-05],
       [-1.48347409e-02, -1.78131332e-05, -5.71104539e-02],
       [-1.53979093e-04,  6.73255729e-03, -1.25948223e-04],
       [ 1.06996796e-02,  8.43651512e-06,  4.40602622e-02],
       [-4.71890717e-05,  6.32167478e-03,  3.81158017e-06],
       [ 4.48193591e-06,  8.42084255e-02,  7.87158316e-06],
       [-1.83483852e-01, -2.14284289e-05, -1.80734895e-02],
       [-1.31189164e-04, -7.22628511e-06, -9.89687680e-04],
       [ 1.43215688e-05,  1.19058396e-03,  2.91719105e-07],
       [-2.35039724e-07, -3.07509368e-02,  2.76205279e-05],
       [-1.01946808e-01,  1.91655064e-05, -1.30614853e-02],
       [ 8.36250834e-05, -1.14359328e-06,  5.66312984e-04],
       [ 5.87601332e-06, -3.65390695e-04,  1.19138272e-06],
       [-5.92517513e-07,  1.86047146e-02, -2.09653079e-05],
       [ 3.75886569e-02, -1.48137973e-05,  5.49797299e-03],
       [-6.85247310e-02,  3.40999287e-03, -4.65853636e-01],
       [-7.56355336e-05, -7.29345098e-02, -2.53077149e-04],
       [-1.86580432e-02,  1.13900019e-04, -2.90335154e-02],
       [ 1.39397913e-03,  8.65145149e-01, -2.54570038e-04],
       [-9.99218972e-02,  1.86348483e-03,  4.82284256e-01],
       [ 3.15008710e-06, -3.08728983e-03, -9.05462719e-05],
       [-1.46776842e-01,  2.23588932e-03,  6.08153461e-01],
       [-1.11595024e-07,  2.27723587e-03,  1.43950188e-05],
       [ 1.23482471e-02, -1.56895579e-05, -1.44816209e-02],
       [-2.55982666e-05,  4.12929452e-07,  6.10567226e-05],
       [ 7.99755710e-08, -2.21573042e-05, -2.69768322e-07],
       [ 1.11739283e-05,  6.51021207e-07, -2.66671560e-05],
       [ 1.18043824e-06, -8.85689338e-06, -2.09675240e-06],
       [ 3.06844027e-06,  1.47404369e-06, -7.26955209e-06],
       [-1.37120745e-06,  3.44331187e-06,  3.30603395e-06],
       [-1.30628059e-05,  2.64196975e-02,  6.98450016e-05],
       [-3.52765620e-02, -7.51672278e-05,  6.54334413e-03],
       [-1.85363280e-05, -4.37833082e-02,  1.24391135e-04],
       [-8.13153559e-02, -9.97229279e-05,  3.13193089e-02],
       [-4.47846441e-03,  9.23771856e-05, -1.87573957e-02],
       [-5.16177408e-06, -4.36481401e-03,  2.30879914e-05],
       [-4.25148397e-04, -6.43732362e-02, -5.23362063e-04],
       [-9.68911343e-06, -5.19064040e-02,  5.36082966e-05],
       [ 6.49838365e-02,  2.13928699e-04, -6.24674321e-03],
       [ 4.12303642e-03, -6.24443157e-04,  3.17333805e-02],
       [-4.58212913e-05,  1.04223568e-02, -1.01009981e-04],
       [-1.83180626e-03,  3.58539442e-01, -1.05403532e-02],
       [-2.00010886e-02,  2.08888831e-04,  6.62867389e-03],
       [-6.19501562e-03,  4.54144136e-01, -5.06666230e-01],
       [-1.04138906e-03, -4.16163940e-01, -5.62174126e-01],
       [ 2.68925872e-05,  2.96018454e-06, -3.36398406e-03],
       [ 1.00469640e-04, -1.39856380e-02, -3.26242657e-04],
       [-6.28487149e-03, -7.19418136e-03,  1.03510786e-04],
       [-3.05564236e-02,  1.71994925e-03,  1.28745949e-03],
       [-1.15250146e-04, -1.14614051e-04,  8.87244104e-04],
       [ 1.37635485e-04,  7.90883916e-04,  1.51137427e-04],
       [ 1.18025519e-06, -2.54396744e-05, -6.45300292e-05],
       [ 4.38111488e-04, -9.82827840e-06, -3.37070889e-03],
       [ 6.54785673e-06, -1.83665154e-05, -2.53611865e-05],
       [-5.03591213e-03,  6.52755467e-05,  1.43874748e-03],
       [-4.56822448e-03,  9.60119925e-05,  2.52845759e-02],
       [-7.88886917e-05, -1.16082698e-03,  5.89776536e-04],
       [ 5.76344055e-04,  3.60458453e-05, -2.55075094e-03],
       [ 1.72154996e-04, -1.13530308e-03, -8.75345368e-05],
       [-5.17047079e-05, -2.72712316e-04,  9.02754888e-06],
       [-5.48662967e-03,  2.41497792e-05, -3.71796245e-05],
       [-5.43763426e-03,  3.67969792e-05,  1.51717244e-04],
       [ 3.16665166e-04,  5.47824113e-04, -1.80489011e-05],
       [-1.26167922e-06,  3.07567335e-06,  1.14094072e-06],
       [ 4.14521239e-06, -1.03951839e-05, -1.00815863e-07],
       [-2.24515711e-05,  3.15992493e-06,  5.98264740e-05],
       [ 9.83043266e-06, -1.48153437e-05,  4.49493788e-06],
       [-2.21945347e-05, -2.90223811e-07,  6.04587329e-05],
       [-3.30253879e-06,  8.92002384e-06, -5.38069357e-08],
       [ 2.42214845e-01,  1.51380048e-03,  1.48982058e-02],
       [ 8.88130327e-05,  2.30452310e-02, -2.09959439e-04],
       [-1.19523462e+00, -6.31027599e-03, -8.10240028e-02],
       [ 1.49842469e-03, -7.25650712e-03,  2.05116773e-04],
       [ 2.36070000e-02,  1.82710842e-04,  3.84782551e-03],
       [ 2.90504558e-03, -1.68194176e-02,  3.06401833e-04],
       [-1.35999024e-02, -1.29658136e-04,  1.19149703e-02],
       [ 1.55655200e-04, -1.87945698e-02,  1.60633689e-03],
       [-2.14830552e-02,  1.00140950e-03,  1.52573969e-02],
       [-3.16815740e-04,  5.64301823e-04,  4.62003582e-04],
       [ 5.69354319e-04,  3.10092080e-04, -3.36784670e-04],
       [-1.11993002e-03,  5.85363133e-04,  1.41289488e-02],
       [ 5.48897635e-04,  6.50794081e-04, -3.10258420e-04],
       [ 4.97233880e-06, -9.84718809e-06,  2.62787566e-06],
       [ 4.91006935e-10, -1.12226625e-09,  2.22904938e-10],
       [ 4.91886108e-05, -2.26871063e-04, -2.12826975e-04],
       [ 1.50510109e-04,  5.13214431e-05, -1.28724122e-04],
       [ 6.31766926e-04,  1.76957401e-04, -1.08919793e-03],
       [ 6.18069550e-03,  3.26456395e-04, -8.51951324e-03],
       [ 1.22372145e-03,  1.99301232e-04, -2.19216897e-03],
       [ 1.77441162e-03,  1.68677787e-05, -2.05706145e-03],
       [-4.97650840e-03, -1.14165324e-02,  9.99460884e-03],
       [ 1.23302503e-02, -3.59909663e-03, -2.23649056e-02],
       [ 1.54304705e-02,  1.62280575e-03, -3.03532464e-02],
       [-4.90308070e-04,  4.25891375e-03,  6.43899568e-04],
       [ 2.02526523e-02,  4.39042712e-03, -4.60487481e-02],
       [-1.06185061e-03,  1.48462946e-02,  1.32411098e-03],
       [-7.52956835e-02, -1.40325141e-02,  1.73151318e-01],
       [ 2.02177627e-03, -3.90243950e-02, -1.84518907e-03],
       [ 1.03889712e-01,  5.18872883e-01, -3.16243021e-01],
       [-1.93459009e-01,  3.27782357e-01,  5.07350553e-01],
       [-3.29766073e-05,  8.50289506e-05,  8.90302361e-05],
       [-1.48822060e-02,  1.29639218e-03,  2.64671090e-02],
       [-2.74979246e-04,  1.36250303e-02,  2.06981759e-04],
       [-9.15511148e-03, -3.23251698e-04,  1.40754403e-02],
       [-1.27311901e-03,  3.40818740e-03,  8.42880181e-04],
       [-1.13318408e-02,  5.45523956e-04,  7.71102775e-02],
       [-1.00548576e-07, -2.88184051e-04, -3.98603099e-05],
       [ 5.55210236e-03, -2.51191821e-04, -6.56101468e-03],
       [ 9.21877656e-02,  3.80238784e-04, -8.22406368e-03],
       [ 2.67133622e-03, -5.33356270e-02, -7.08001251e-04],
       [-3.97496091e-05,  2.72289047e-03,  8.59664273e-06],
       [ 1.05520227e-03,  1.05179905e-04,  1.10920878e-02],
       [ 4.29974976e-03,  1.56947122e-02, -2.70188960e-03],
       [ 4.91777965e-05,  6.79733057e-03, -5.65982540e-05],
       [ 5.13074615e-03, -5.13253476e-05, -5.11178898e-03],
       [-2.64833717e-05,  1.26712930e-06,  1.42890362e-05],
       [ 2.79396375e-06,  8.45488018e-06, -1.96376575e-06],
       [ 8.76185666e-06, -1.10273915e-07, -4.72260922e-06],
       [ 6.75059925e-07,  2.71782259e-06, -2.79306576e-07],
       [-2.02090749e-05,  2.77093119e-07,  1.08830779e-05],
       [ 1.79310324e-06,  7.37704975e-06, -8.25382579e-07],
       [-2.37355984e-05,  4.91655748e-07,  1.24009373e-05],
       [-1.79032833e-06, -6.71734779e-06,  7.42561015e-07],
       [ 2.03050123e-05, -2.26881036e-07, -1.05936945e-05],
       [ 1.78882389e-06,  7.61334878e-06, -6.22784402e-07],
       [-2.14372204e-07,  7.45107837e-08,  1.10796411e-07],
       [ 1.99371820e-08, -1.26083777e-07, -9.17075723e-08],
       [ 9.35696089e-03, -1.58981849e-04, -2.83684344e-02]]))
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],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 7.07573879e-07,  1.41283728e-01,  6.53919496e-06],
       [-5.06620672e-01, -1.19383139e-04, -3.62765895e-02],
       [-1.17894505e-10, -7.42090778e-10, -1.93602816e-11],
       [-8.14819266e-06, -1.10515849e-02, -1.72126665e-06],
       [-2.83747070e-06, -1.79995424e-02, -3.91652814e-06],
       [-4.38729147e-01, -9.62770869e-05, -3.00230737e-02],
       [ 3.64946244e-02,  2.39596452e-05,  7.94026055e-02],
       [ 6.56409965e-06, -1.61562545e-03,  4.60557000e-05],
       [-1.48347409e-02, -1.78131332e-05, -5.71104539e-02],
       [-1.53979093e-04,  6.73255729e-03, -1.25948223e-04],
       [ 1.06996796e-02,  8.43651512e-06,  4.40602622e-02],
       [-4.71890717e-05,  6.32167478e-03,  3.81158017e-06],
       [ 4.48193591e-06,  8.42084255e-02,  7.87158316e-06],
       [-1.83483852e-01, -2.14284289e-05, -1.80734895e-02],
       [-1.31189164e-04, -7.22628511e-06, -9.89687680e-04],
       [ 1.43215688e-05,  1.19058396e-03,  2.91719105e-07],
       [-2.35039724e-07, -3.07509368e-02,  2.76205279e-05],
       [-1.01946808e-01,  1.91655064e-05, -1.30614853e-02],
       [ 8.36250834e-05, -1.14359328e-06,  5.66312984e-04],
       [ 5.87601332e-06, -3.65390695e-04,  1.19138272e-06],
       [-5.92517513e-07,  1.86047146e-02, -2.09653079e-05],
       [ 3.75886569e-02, -1.48137973e-05,  5.49797299e-03],
       [-6.85247310e-02,  3.40999287e-03, -4.65853636e-01],
       [-7.56355336e-05, -7.29345098e-02, -2.53077149e-04],
       [-1.86580432e-02,  1.13900019e-04, -2.90335154e-02],
       [ 1.39397913e-03,  8.65145149e-01, -2.54570038e-04],
       [-9.99218972e-02,  1.86348483e-03,  4.82284256e-01],
       [ 3.15008710e-06, -3.08728983e-03, -9.05462719e-05],
       [-1.46776842e-01,  2.23588932e-03,  6.08153461e-01],
       [-1.11595024e-07,  2.27723587e-03,  1.43950188e-05],
       [ 1.23482471e-02, -1.56895579e-05, -1.44816209e-02],
       [-2.55982666e-05,  4.12929452e-07,  6.10567226e-05],
       [ 7.99755710e-08, -2.21573042e-05, -2.69768322e-07],
       [ 1.11739283e-05,  6.51021207e-07, -2.66671560e-05],
       [ 1.18043824e-06, -8.85689338e-06, -2.09675240e-06],
       [ 3.06844027e-06,  1.47404369e-06, -7.26955209e-06],
       [-1.37120745e-06,  3.44331187e-06,  3.30603395e-06],
       [-1.30628059e-05,  2.64196975e-02,  6.98450016e-05],
       [-3.52765620e-02, -7.51672278e-05,  6.54334413e-03],
       [-1.85363280e-05, -4.37833082e-02,  1.24391135e-04],
       [-8.13153559e-02, -9.97229279e-05,  3.13193089e-02],
       [-4.47846441e-03,  9.23771856e-05, -1.87573957e-02],
       [-5.16177408e-06, -4.36481401e-03,  2.30879914e-05],
       [-4.25148397e-04, -6.43732362e-02, -5.23362063e-04],
       [-9.68911343e-06, -5.19064040e-02,  5.36082966e-05],
       [ 6.49838365e-02,  2.13928699e-04, -6.24674321e-03],
       [ 4.12303642e-03, -6.24443157e-04,  3.17333805e-02],
       [-4.58212913e-05,  1.04223568e-02, -1.01009981e-04],
       [-1.83180626e-03,  3.58539442e-01, -1.05403532e-02],
       [-2.00010886e-02,  2.08888831e-04,  6.62867389e-03],
       [-6.19501562e-03,  4.54144136e-01, -5.06666230e-01],
       [-1.04138906e-03, -4.16163940e-01, -5.62174126e-01],
       [ 2.68925872e-05,  2.96018454e-06, -3.36398406e-03],
       [ 1.00469640e-04, -1.39856380e-02, -3.26242657e-04],
       [-6.28487149e-03, -7.19418136e-03,  1.03510786e-04],
       [-3.05564236e-02,  1.71994925e-03,  1.28745949e-03],
       [-1.15250146e-04, -1.14614051e-04,  8.87244104e-04],
       [ 1.37635485e-04,  7.90883916e-04,  1.51137427e-04],
       [ 1.18025519e-06, -2.54396744e-05, -6.45300292e-05],
       [ 4.38111488e-04, -9.82827840e-06, -3.37070889e-03],
       [ 6.54785673e-06, -1.83665154e-05, -2.53611865e-05],
       [-5.03591213e-03,  6.52755467e-05,  1.43874748e-03],
       [-4.56822448e-03,  9.60119925e-05,  2.52845759e-02],
       [-7.88886917e-05, -1.16082698e-03,  5.89776536e-04],
       [ 5.76344055e-04,  3.60458453e-05, -2.55075094e-03],
       [ 1.72154996e-04, -1.13530308e-03, -8.75345368e-05],
       [-5.17047079e-05, -2.72712316e-04,  9.02754888e-06],
       [-5.48662967e-03,  2.41497792e-05, -3.71796245e-05],
       [-5.43763426e-03,  3.67969792e-05,  1.51717244e-04],
       [ 3.16665166e-04,  5.47824113e-04, -1.80489011e-05],
       [-1.26167922e-06,  3.07567335e-06,  1.14094072e-06],
       [ 4.14521239e-06, -1.03951839e-05, -1.00815863e-07],
       [-2.24515711e-05,  3.15992493e-06,  5.98264740e-05],
       [ 9.83043266e-06, -1.48153437e-05,  4.49493788e-06],
       [-2.21945347e-05, -2.90223811e-07,  6.04587329e-05],
       [-3.30253879e-06,  8.92002384e-06, -5.38069357e-08],
       [ 2.42214845e-01,  1.51380048e-03,  1.48982058e-02],
       [ 8.88130327e-05,  2.30452310e-02, -2.09959439e-04],
       [-1.19523462e+00, -6.31027599e-03, -8.10240028e-02],
       [ 1.49842469e-03, -7.25650712e-03,  2.05116773e-04],
       [ 2.36070000e-02,  1.82710842e-04,  3.84782551e-03],
       [ 2.90504558e-03, -1.68194176e-02,  3.06401833e-04],
       [-1.35999024e-02, -1.29658136e-04,  1.19149703e-02],
       [ 1.55655200e-04, -1.87945698e-02,  1.60633689e-03],
       [-2.14830552e-02,  1.00140950e-03,  1.52573969e-02],
       [-3.16815740e-04,  5.64301823e-04,  4.62003582e-04],
       [ 5.69354319e-04,  3.10092080e-04, -3.36784670e-04],
       [-1.11993002e-03,  5.85363133e-04,  1.41289488e-02],
       [ 5.48897635e-04,  6.50794081e-04, -3.10258420e-04],
       [ 4.97233880e-06, -9.84718809e-06,  2.62787566e-06],
       [ 4.91006935e-10, -1.12226625e-09,  2.22904938e-10],
       [ 4.91886108e-05, -2.26871063e-04, -2.12826975e-04],
       [ 1.50510109e-04,  5.13214431e-05, -1.28724122e-04],
       [ 6.31766926e-04,  1.76957401e-04, -1.08919793e-03],
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        -1.76012875e-05,  9.06834379e-08, -3.82172713e-10,
        -3.96270034e-08, -3.02492336e-09, -1.08094339e-08,
         4.91234942e-09,  9.54423109e-08,  5.05467516e-06,
         1.77562237e-07,  3.82554088e-05, -2.51229785e-05,
         3.56476526e-08, -8.83263641e-07,  9.09624629e-08,
        -7.53043724e-06,  8.53320903e-05, -1.49022152e-07,
        -1.85860130e-05,  1.09945079e-05, -8.94019667e-04,
        -9.91973087e-04, -6.00595030e-06, -5.75536815e-07,
        -1.23494514e-07,  8.02725336e-07,  1.64386790e-06,
         2.88944269e-07, -1.21108638e-07, -6.27180083e-06,
        -4.68389793e-08,  2.50215901e-06,  4.70329142e-05,
         1.10435274e-06, -4.73063451e-06, -1.51250943e-07,
         1.32493476e-08, -1.71761209e-07,  5.50403092e-08,
        -1.89612384e-08,  2.02546844e-09,  1.04779869e-10,
         1.09753312e-07,  9.03964386e-09,  1.10946157e-07,
        -3.39508108e-10,  3.30583953e-05, -3.72334871e-07,
        -1.66114655e-04,  3.74194923e-07,  6.65284692e-06,
         6.10007888e-07,  1.64450407e-05,  2.36124986e-06,
         2.04180832e-05,  6.99112250e-07, -4.15903333e-07,
         2.30371301e-05, -3.92045403e-07,  4.06221986e-09,
         3.22409239e-13, -3.33940619e-07, -1.69489017e-07,
        -1.51041693e-06, -1.13287823e-05, -3.07001085e-06,
        -2.63375754e-06,  1.33080317e-05, -2.96808182e-05,
        -4.02430861e-05,  8.39502685e-07, -6.08060209e-05,
         1.70456150e-06,  2.28508206e-04, -2.32314374e-06,
        -4.16471774e-04,  6.64653169e-04,  9.21452529e-08,
         2.68439262e-05,  2.38409237e-07,  1.76670447e-05,
         8.42700039e-07,  1.05398093e-04, -1.05145953e-08,
        -3.18629380e-06, -7.39155916e-06, -7.09017061e-07,
         3.95902467e-09,  1.38654877e-05, -2.51206809e-06,
        -5.99991204e-08, -6.22158297e-06, -1.72927313e-08,
        -1.48064498e-09,  5.73342114e-09, -2.66337055e-11,
        -1.32409630e-08, -3.59520068e-10, -1.63987147e-08,
         8.43765021e-11,  1.40551094e-08, -1.61746748e-10,
        -1.47317575e-10, -1.20631847e-10, -5.78118957e-05]]))
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.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [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.],
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       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
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       [0.],
       [0.],
       [0.],
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       [0.],
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       [0.],
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       [0.],
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       [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.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [0.],
       [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.],
       [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.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.],
       [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., 1., 0.],
       [0., 0., 1.]]))
D21_nv = sp.Matrix(np.array([[0.  ],
       [0.  ],
       [0.05]]))


# ---------- create symbolic parameter functions
# parameter values can be constant/fixed values OR set in relation to other parameters (for example: a = 2*b)  


# list of symbolic parameter functions
# tailing "_sf" stands for "symbolic parameter function"
pp_sf = [A_nv, B_nv, B1_nv, C1_nv, C_nv, D11_nv, D12_nv, D21_nv]


#  ---------- list for substitution
# -- entries are tuples like: (independent symbolic parameter, numerical value)
pp_subs_list = []


# OPTONAL: Dictionary which defines how certain variables shall be written
# in the table - key: Symbolic Variable, Value: LaTeX Representation/Code
# useful for example for complex variables: {Z: r"\underline{Z}"}
latex_names = {}


# ---------- Define LaTeX table

# Define table header 
# DON'T CHANGE FOLLOWING ENTRIES: "Symbol", "Value"
tabular_header = ["Symbol", "Value"]

# Define column text alignments
col_alignment = ["center", "left"]


# Define Entries of all columns before the Symbol-Column
# --- Entries need to be latex code
col_1 = [] 

# contains all lists of the columns before the "Symbol" Column
# --- Empty list, if there are no columns before the "Symbol" Column
start_columns_list = []


# Define Entries of the columns after the Value-Column
# --- Entries need to be latex code
col_4 = []

# contains all lists of columns after the FIX ENTRIES
# --- Empty list, if there are no columns after the "Value" column
end_columns_list = []