Automatic Control Knowledge Repository

# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:54:07).

import numpy as np
import system_model
from scipy.integrate import solve_ivp, odeint

from ackrep_core import ResultContainer
from ackrep_core.system_model_management import save_plot_in_dir
import matplotlib.pyplot as plt
import os
from ipydex import Container

# link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html


def simulate():
    """
    simulate the system model with scipy.integrate.solve_ivp

    :return: result of solve_ivp, might contains input function
    """

    model = system_model.Model()

    rhs_xx_pp_symb = model.get_rhs_symbolic()
    rhs = model.get_rhs_func()

    # initial state values
    xx0 = np.ones(model.sys_dim)

    t_end = 10
    tt = np.linspace(0, t_end, 1000)

    simulation_data = solve_ivp(rhs, (0, t_end), xx0, t_eval=tt)

    # using odeint for models with large state vectors
    # res = odeint(rhs, y0=xx0, t=tt, tfirst=True)
    # simulation_data = Container()
    # simulation_data.y = res.transpose()
    # simulation_data.t = tt

    # postprocessing: calc output
    ny = 2
    C = model.get_parameter_value("C")
    D21 = model.get_parameter_value("D21")
    output = np.zeros((ny, len(tt)))
    for i in range(len(tt)):
        output[:,i] = np.matmul(C, simulation_data.y[:,i]) # + np.matmul(D21, w)
    simulation_data.output = output

    save_plot(simulation_data)

    return simulation_data


def save_plot(simulation_data):
    """
    plot your data and save the plot
    access to data via: simulation_data.t   array of time values
                        simulation_data.y   array of data components
                        simulation_data.uu  array of input values

    :param simulation_data: simulation_data of system_model
    :return: None
    """

    for i in range(simulation_data.output.shape[0]):
        plt.plot(simulation_data.t, simulation_data.output[i], label=f"$y_{i}$")

    plt.legend()
    plt.tight_layout()

    save_plot_in_dir()


def evaluate_simulation(simulation_data):
    """
    assert that the simulation results are as expected

    :param simulation_data: simulation_data of system_model
    :return:
    """
    expected_final_state = np.zeros(120)

    rc = ResultContainer(score=1.0)
    simulated_final_state = simulation_data.y[:, -1]
    rc.final_state_errors = [
        simulated_final_state[i] - expected_final_state[i] for i in np.arange(0, len(simulated_final_state))
    ]
    rc.success = np.allclose(expected_final_state, simulated_final_state, rtol=0, atol=1e-2)

    return rc

# This file was autogenerated from the template: system_model.py.template (2022-10-10 15:54:07).

import sympy as sp
import numpy as np
import symbtools as st
import importlib
import sys, os
#from ipydex import IPS, activate_ips_on_exception  

from ackrep_core.system_model_management import GenericModel, import_parameters

# Import parameter_file
params = import_parameters()


#link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html


class Model(GenericModel): 

    def initialize(self):
        """
        this function is called by the constructor of GenericModel

        :return: None
        """

        # Define number of inputs -- MODEL DEPENDENT
        self.u_dim = 1

        # Set "sys_dim" to constant value, if system dimension is constant 
        self.sys_dim = 120

        # check existence of params file
        self.has_params = True
        self.params = params
        

    # ----------- SET DEFAULT INPUT FUNCTION ---------- # 
    def uu_default_func(self):
        """
        define input function
    
        :return:(function with 2 args - t, xx_nv) default input function 
        """ 
        
        def uu_rhs(t, xx_nv):
            """
            sequence of numerical input values

            :param t:(scalar or vector) time
            :param xx_nv:(vector or array of vectors) numeric state vector
            :return:(list) numeric inputs 
            """ 
            u = np.zeros(self.u_dim)
            return u

        return uu_rhs


    # ----------- SYMBOLIC RHS FUNCTION ---------- # 

    def get_rhs_symbolic(self):
        """
        define symbolic rhs function

        :return: matrix of symbolic rhs-functions
        """
        if self.dxx_dt_symb is not None:
            return self.dxx_dt_symb

        x = self.xx_symb  
        A, B, B1, C1, C, D11, D12, D21 = self.pp_symb   # parameters
        w = np.zeros(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 15:54:08).

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 = 'Linear cable mass problem of order 20'


# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 120, 120)
B = sp.MatrixSymbol('B', 120, 1)
B1 = sp.MatrixSymbol('B1', 120, 1)
C1 = sp.MatrixSymbol('C1', 3, 120)
C = sp.MatrixSymbol('C', 2, 120)
D11 = sp.MatrixSymbol('D11', 3, 1)
D12 = sp.MatrixSymbol('D12', 3, 1)
D21 = sp.MatrixSymbol('D21', 2, 1)

pp_symb = [A, B, B1, C1, C, D11, D12, D21]


# ---------- create auxiliary symbolic parameters 

# set numerical values of auxiliary parameters
# trailing "_nv" stands for "numerical value"
A_nv = sp.Matrix(np.array([[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         1.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  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,
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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,
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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,
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        -4.28034774e-04,  1.59744752e-03, -1.25986714e-03]]))
B_nv = sp.Matrix(np.array([[ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [-1.65943662e-34],
       [ 6.63774646e-34],
       [-2.48915492e-33],
       [ 9.29284505e-33],
       [-3.46822253e-32],
       [ 1.29436056e-31],
       [-4.83061999e-31],
       [ 1.80281194e-30],
       [-6.72818576e-30],
       [ 2.51099311e-29],
       [-9.37115386e-29],
       [ 3.49736223e-28],
       [-1.30523336e-27],
       [ 4.87119720e-27],
       [-1.81795554e-26],
       [ 6.78470245e-26],
       [-2.53208543e-25],
       [ 9.44987146e-25],
       [-3.52674004e-24],
       [ 1.31619730e-23],
       [-4.91211521e-23],
       [ 1.83322635e-22],
       [-6.84169389e-22],
       [ 2.55335492e-21],
       [-9.52925029e-21],
       [ 3.55636462e-20],
       [-1.32725335e-19],
       [ 4.95337692e-19],
       [-1.84862543e-18],
       [ 6.89916405e-18],
       [-2.57480308e-17],
       [ 9.60929590e-17],
       [-3.58623805e-16],
       [ 1.33840226e-15],
       [-4.99498524e-15],
       [ 1.86415387e-14],
       [-6.95711696e-14],
       [ 2.59643140e-13],
       [-9.69001389e-13],
       [ 3.61636242e-12],
       [-1.34964483e-11],
       [ 5.03694307e-11],
       [-1.87981274e-10],
       [ 7.01555667e-10],
       [-2.61824139e-09],
       [ 9.77140991e-09],
       [-3.64673982e-08],
       [ 1.36098183e-07],
       [-5.07925334e-07],
       [ 1.89560315e-06],
       [-7.07448728e-06],
       [ 2.64023460e-05],
       [-9.85348965e-05],
       [ 3.67737240e-04],
       [-1.37241406e-03],
       [ 5.12191902e-03],
       [-1.91152620e-02],
       [ 7.13391290e-02],
       [-2.66241254e-01],
       [ 9.93625887e-01]]))
B1_nv = sp.Matrix(np.array([[ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [ 0.00000000e+00],
       [-1.65943662e-34],
       [ 6.63774646e-34],
       [-2.48915492e-33],
       [ 9.29284505e-33],
       [-3.46822253e-32],
       [ 1.29436056e-31],
       [-4.83061999e-31],
       [ 1.80281194e-30],
       [-6.72818576e-30],
       [ 2.51099311e-29],
       [-9.37115386e-29],
       [ 3.49736223e-28],
       [-1.30523336e-27],
       [ 4.87119720e-27],
       [-1.81795554e-26],
       [ 6.78470245e-26],
       [-2.53208543e-25],
       [ 9.44987146e-25],
       [-3.52674004e-24],
       [ 1.31619730e-23],
       [-4.91211521e-23],
       [ 1.83322635e-22],
       [-6.84169389e-22],
       [ 2.55335492e-21],
       [-9.52925029e-21],
       [ 3.55636462e-20],
       [-1.32725335e-19],
       [ 4.95337692e-19],
       [-1.84862543e-18],
       [ 6.89916405e-18],
       [-2.57480308e-17],
       [ 9.60929590e-17],
       [-3.58623805e-16],
       [ 1.33840226e-15],
       [-4.99498524e-15],
       [ 1.86415387e-14],
       [-6.95711696e-14],
       [ 2.59643140e-13],
       [-9.69001389e-13],
       [ 3.61636242e-12],
       [-1.34964483e-11],
       [ 5.03694307e-11],
       [-1.87981274e-10],
       [ 7.01555667e-10],
       [-2.61824139e-09],
       [ 9.77140991e-09],
       [-3.64673982e-08],
       [ 1.36098183e-07],
       [-5.07925334e-07],
       [ 1.89560315e-06],
       [-7.07448728e-06],
       [ 2.64023460e-05],
       [-9.85348965e-05],
       [ 3.67737240e-04],
       [-1.37241406e-03],
       [ 5.12191902e-03],
       [-1.91152620e-02],
       [ 7.13391290e-02],
       [-2.66241254e-01],
       [ 9.93625887e-01]]))
C1_nv = sp.Matrix(np.array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 1.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0.]]))
C_nv = sp.Matrix(np.array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 1.]]))
D11_nv = sp.Matrix(np.array([[0.],
       [0.],
       [0.]]))
D12_nv = sp.Matrix(np.array([[0.        ],
       [0.        ],
       [1.22474487]]))
D21_nv = sp.Matrix(np.array([[0.],
       [1.]]))


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


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


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


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


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

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

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


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

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


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

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