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Details for: "Euler-Bernoulli Beam"

Steps for local reproduction
Name: Euler-Bernoulli Beam (Key: COM56)
Path: ackrep_data/system_models/compleib_models/EB6 View on GitHub
Type: system_model
Short Description: EB6 Euler-Bernoulli Beam like EB2 very low damping --> xi=1e-7 higher dimension s_max=80 --> nx=160
Created: 2022-10-10 15:53:56
Compatible Environment: default_conda_environment (Key: CDAMA)
Source Code [ / ] simulation.py 
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:53:57).

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 = 1
    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(160)

    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 15:53:57).

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 = 160

        # 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(2) # 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 15:53:57).

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 = 'Euler-Bernoulli Beam'


# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 160, 160)
B = sp.MatrixSymbol('B', 160, 1)
B1 = sp.MatrixSymbol('B1', 160, 2)
C1 = sp.MatrixSymbol('C1', 2, 160)
C = sp.MatrixSymbol('C', 1, 160)
D11 = sp.MatrixSymbol('D11', 2, 2)
D12 = sp.MatrixSymbol('D12', 2, 1)
D21 = sp.MatrixSymbol('D21', 1, 2)

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([[ 0.0000000e+00,  1.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
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         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
         0.0000000e+00,  0.0000000e+00, -4.0960000e+07, -1.2800000e-03]]))
B_nv = sp.Matrix(np.array([[ 0.00000000e+00],
       [ 9.87684580e-01],
       [ 0.00000000e+00],
       [-3.09062722e-01],
       [ 0.00000000e+00],
       [-8.90973779e-01],
       [ 0.00000000e+00],
       [ 5.87863046e-01],
       [ 0.00000000e+00],
       [ 7.07021780e-01],
       [ 0.00000000e+00],
       [-8.09101770e-01],
       [ 0.00000000e+00],
       [-4.53840551e-01],
       [ 0.00000000e+00],
       [ 9.51115930e-01],
       [ 0.00000000e+00],
       [ 1.56220760e-01],
       [ 0.00000000e+00],
       [-9.99999971e-01],
       [ 0.00000000e+00],
       [ 1.56695650e-01],
       [ 0.00000000e+00],
       [ 9.50967330e-01],
       [ 0.00000000e+00],
       [-4.54268941e-01],
       [ 0.00000000e+00],
       [-8.08819119e-01],
       [ 0.00000000e+00],
       [ 7.07361723e-01],
       [ 0.00000000e+00],
       [ 5.87474022e-01],
       [ 0.00000000e+00],
       [-8.91191991e-01],
       [ 0.00000000e+00],
       [-3.08605415e-01],
       [ 0.00000000e+00],
       [ 9.87759692e-01],
       [ 0.00000000e+00],
       [-4.80810494e-04],
       [ 0.00000000e+00],
       [-9.87609239e-01],
       [ 0.00000000e+00],
       [ 3.09519957e-01],
       [ 0.00000000e+00],
       [ 8.90755362e-01],
       [ 0.00000000e+00],
       [-5.88251935e-01],
       [ 0.00000000e+00],
       [-7.06681673e-01],
       [ 0.00000000e+00],
       [ 8.09384234e-01],
       [ 0.00000000e+00],
       [ 4.53412057e-01],
       [ 0.00000000e+00],
       [-9.51264311e-01],
       [ 0.00000000e+00],
       [-1.55745835e-01],
       [ 0.00000000e+00],
       [ 9.99999740e-01],
       [ 0.00000000e+00],
       [-1.57170502e-01],
       [ 0.00000000e+00],
       [-9.50818509e-01],
       [ 0.00000000e+00],
       [ 4.54697226e-01],
       [ 0.00000000e+00],
       [ 8.08536282e-01],
       [ 0.00000000e+00],
       [-7.07701503e-01],
       [ 0.00000000e+00],
       [-5.87084861e-01],
       [ 0.00000000e+00],
       [ 8.91409996e-01],
       [ 0.00000000e+00],
       [ 3.08148037e-01],
       [ 0.00000000e+00],
       [-9.87834576e-01],
       [ 0.00000000e+00],
       [ 9.61620876e-04],
       [ 0.00000000e+00],
       [ 9.87533669e-01],
       [ 0.00000000e+00],
       [-3.09977120e-01],
       [ 0.00000000e+00],
       [-8.90536739e-01],
       [ 0.00000000e+00],
       [ 5.88640688e-01],
       [ 0.00000000e+00],
       [ 7.06341403e-01],
       [ 0.00000000e+00],
       [-8.09666510e-01],
       [ 0.00000000e+00],
       [-4.52983458e-01],
       [ 0.00000000e+00],
       [ 9.51412472e-01],
       [ 0.00000000e+00],
       [ 1.55270874e-01],
       [ 0.00000000e+00],
       [-9.99999278e-01],
       [ 0.00000000e+00],
       [ 1.57645319e-01],
       [ 0.00000000e+00],
       [ 9.50669469e-01],
       [ 0.00000000e+00],
       [-4.55125405e-01],
       [ 0.00000000e+00],
       [-8.08253257e-01],
       [ 0.00000000e+00],
       [ 7.08041120e-01],
       [ 0.00000000e+00],
       [ 5.86695565e-01],
       [ 0.00000000e+00],
       [-8.91627795e-01],
       [ 0.00000000e+00],
       [-3.07690588e-01],
       [ 0.00000000e+00],
       [ 9.87909232e-01],
       [ 0.00000000e+00],
       [-1.44243104e-03],
       [ 0.00000000e+00],
       [-9.87457872e-01],
       [ 0.00000000e+00],
       [ 3.10434212e-01],
       [ 0.00000000e+00],
       [ 8.90317910e-01],
       [ 0.00000000e+00],
       [-5.89029304e-01],
       [ 0.00000000e+00],
       [-7.06000969e-01],
       [ 0.00000000e+00],
       [ 8.09948600e-01],
       [ 0.00000000e+00],
       [ 4.52554754e-01],
       [ 0.00000000e+00],
       [-9.51560413e-01],
       [ 0.00000000e+00],
       [-1.54795877e-01],
       [ 0.00000000e+00],
       [ 9.99998584e-01],
       [ 0.00000000e+00],
       [-1.58120099e-01],
       [ 0.00000000e+00],
       [-9.50520209e-01],
       [ 0.00000000e+00],
       [ 4.55553479e-01],
       [ 0.00000000e+00],
       [ 8.07970045e-01],
       [ 0.00000000e+00],
       [-7.08380573e-01],
       [ 0.00000000e+00],
       [-5.86306133e-01],
       [ 0.00000000e+00],
       [ 8.91845388e-01],
       [ 0.00000000e+00],
       [ 3.07233068e-01],
       [ 0.00000000e+00],
       [-9.87983660e-01],
       [ 0.00000000e+00],
       [ 1.92324086e-03]]))
B1_nv = sp.Matrix(np.array([[ 0.00000000e+00],
       [ 9.87684580e-01],
       [ 0.00000000e+00],
       [-3.09062722e-01],
       [ 0.00000000e+00],
       [-8.90973779e-01],
       [ 0.00000000e+00],
       [ 5.87863046e-01],
       [ 0.00000000e+00],
       [ 7.07021780e-01],
       [ 0.00000000e+00],
       [-8.09101770e-01],
       [ 0.00000000e+00],
       [-4.53840551e-01],
       [ 0.00000000e+00],
       [ 9.51115930e-01],
       [ 0.00000000e+00],
       [ 1.56220760e-01],
       [ 0.00000000e+00],
       [-9.99999971e-01],
       [ 0.00000000e+00],
       [ 1.56695650e-01],
       [ 0.00000000e+00],
       [ 9.50967330e-01],
       [ 0.00000000e+00],
       [-4.54268941e-01],
       [ 0.00000000e+00],
       [-8.08819119e-01],
       [ 0.00000000e+00],
       [ 7.07361723e-01],
       [ 0.00000000e+00],
       [ 5.87474022e-01],
       [ 0.00000000e+00],
       [-8.91191991e-01],
       [ 0.00000000e+00],
       [-3.08605415e-01],
       [ 0.00000000e+00],
       [ 9.87759692e-01],
       [ 0.00000000e+00],
       [-4.80810494e-04],
       [ 0.00000000e+00],
       [-9.87609239e-01],
       [ 0.00000000e+00],
       [ 3.09519957e-01],
       [ 0.00000000e+00],
       [ 8.90755362e-01],
       [ 0.00000000e+00],
       [-5.88251935e-01],
       [ 0.00000000e+00],
       [-7.06681673e-01],
       [ 0.00000000e+00],
       [ 8.09384234e-01],
       [ 0.00000000e+00],
       [ 4.53412057e-01],
       [ 0.00000000e+00],
       [-9.51264311e-01],
       [ 0.00000000e+00],
       [-1.55745835e-01],
       [ 0.00000000e+00],
       [ 9.99999740e-01],
       [ 0.00000000e+00],
       [-1.57170502e-01],
       [ 0.00000000e+00],
       [-9.50818509e-01],
       [ 0.00000000e+00],
       [ 4.54697226e-01],
       [ 0.00000000e+00],
       [ 8.08536282e-01],
       [ 0.00000000e+00],
       [-7.07701503e-01],
       [ 0.00000000e+00],
       [-5.87084861e-01],
       [ 0.00000000e+00],
       [ 8.91409996e-01],
       [ 0.00000000e+00],
       [ 3.08148037e-01],
       [ 0.00000000e+00],
       [-9.87834576e-01],
       [ 0.00000000e+00],
       [ 9.61620876e-04],
       [ 0.00000000e+00],
       [ 9.87533669e-01],
       [ 0.00000000e+00],
       [-3.09977120e-01],
       [ 0.00000000e+00],
       [-8.90536739e-01],
       [ 0.00000000e+00],
       [ 5.88640688e-01],
       [ 0.00000000e+00],
       [ 7.06341403e-01],
       [ 0.00000000e+00],
       [-8.09666510e-01],
       [ 0.00000000e+00],
       [-4.52983458e-01],
       [ 0.00000000e+00],
       [ 9.51412472e-01],
       [ 0.00000000e+00],
       [ 1.55270874e-01],
       [ 0.00000000e+00],
       [-9.99999278e-01],
       [ 0.00000000e+00],
       [ 1.57645319e-01],
       [ 0.00000000e+00],
       [ 9.50669469e-01],
       [ 0.00000000e+00],
       [-4.55125405e-01],
       [ 0.00000000e+00],
       [-8.08253257e-01],
       [ 0.00000000e+00],
       [ 7.08041120e-01],
       [ 0.00000000e+00],
       [ 5.86695565e-01],
       [ 0.00000000e+00],
       [-8.91627795e-01],
       [ 0.00000000e+00],
       [-3.07690588e-01],
       [ 0.00000000e+00],
       [ 9.87909232e-01],
       [ 0.00000000e+00],
       [-1.44243104e-03],
       [ 0.00000000e+00],
       [-9.87457872e-01],
       [ 0.00000000e+00],
       [ 3.10434212e-01],
       [ 0.00000000e+00],
       [ 8.90317910e-01],
       [ 0.00000000e+00],
       [-5.89029304e-01],
       [ 0.00000000e+00],
       [-7.06000969e-01],
       [ 0.00000000e+00],
       [ 8.09948600e-01],
       [ 0.00000000e+00],
       [ 4.52554754e-01],
       [ 0.00000000e+00],
       [-9.51560413e-01],
       [ 0.00000000e+00],
       [-1.54795877e-01],
       [ 0.00000000e+00],
       [ 9.99998584e-01],
       [ 0.00000000e+00],
       [-1.58120099e-01],
       [ 0.00000000e+00],
       [-9.50520209e-01],
       [ 0.00000000e+00],
       [ 4.55553479e-01],
       [ 0.00000000e+00],
       [ 8.07970045e-01],
       [ 0.00000000e+00],
       [-7.08380573e-01],
       [ 0.00000000e+00],
       [-5.86306133e-01],
       [ 0.00000000e+00],
       [ 8.91845388e-01],
       [ 0.00000000e+00],
       [ 3.07233068e-01],
       [ 0.00000000e+00],
       [-9.87983660e-01],
       [ 0.00000000e+00],
       [ 1.92324086e-03]]))
C1_nv = sp.Matrix(np.array([[ 8.09025727e-01,  0.00000000e+00, -9.51047333e-01,
         0.00000000e+00,  3.08974603e-01,  0.00000000e+00,
         5.87833331e-01,  0.00000000e+00, -9.99999997e-01,
         0.00000000e+00,  5.87713130e-01,  0.00000000e+00,
         3.09115905e-01,  0.00000000e+00, -9.51093239e-01,
         0.00000000e+00,  8.08938390e-01,  0.00000000e+00,
         1.48575128e-04,  0.00000000e+00, -8.09113047e-01,
         0.00000000e+00,  9.51001406e-01,  0.00000000e+00,
        -3.08833294e-01,  0.00000000e+00, -5.87953519e-01,
         0.00000000e+00,  9.99999975e-01,  0.00000000e+00,
        -5.87592916e-01,  0.00000000e+00, -3.09257200e-01,
         0.00000000e+00,  9.51139124e-01,  0.00000000e+00,
        -8.08851035e-01,  0.00000000e+00, -2.97150253e-04,
         0.00000000e+00,  8.09200349e-01,  0.00000000e+00,
        -9.50955459e-01,  0.00000000e+00,  3.08691979e-01,
         0.00000000e+00,  5.88073694e-01,  0.00000000e+00,
        -9.99999931e-01,  0.00000000e+00,  5.87472689e-01,
         0.00000000e+00,  3.09398489e-01,  0.00000000e+00,
        -9.51184988e-01,  0.00000000e+00,  8.08763662e-01,
         0.00000000e+00,  4.45725371e-04,  0.00000000e+00,
        -8.09287632e-01,  0.00000000e+00,  9.50909490e-01,
         0.00000000e+00, -3.08550656e-01,  0.00000000e+00,
        -5.88193857e-01,  0.00000000e+00,  9.99999865e-01,
         0.00000000e+00, -5.87352449e-01,  0.00000000e+00,
        -3.09539770e-01,  0.00000000e+00,  9.51230831e-01,
         0.00000000e+00, -8.08676271e-01,  0.00000000e+00,
        -5.94300479e-04,  0.00000000e+00,  8.09374898e-01,
         0.00000000e+00, -9.50863500e-01,  0.00000000e+00,
         3.08409327e-01,  0.00000000e+00,  5.88314006e-01,
         0.00000000e+00, -9.99999776e-01,  0.00000000e+00,
         5.87232196e-01,  0.00000000e+00,  3.09681045e-01,
         0.00000000e+00, -9.51276653e-01,  0.00000000e+00,
         8.08588862e-01,  0.00000000e+00,  7.42875574e-04,
         0.00000000e+00, -8.09462146e-01,  0.00000000e+00,
         9.50817489e-01,  0.00000000e+00, -3.08267991e-01,
         0.00000000e+00, -5.88434142e-01,  0.00000000e+00,
         9.99999666e-01,  0.00000000e+00, -5.87111930e-01,
         0.00000000e+00, -3.09822313e-01,  0.00000000e+00,
         9.51322454e-01,  0.00000000e+00, -8.08501435e-01,
         0.00000000e+00, -8.91450653e-04,  0.00000000e+00,
         8.09549377e-01,  0.00000000e+00, -9.50771457e-01,
         0.00000000e+00,  3.08126648e-01,  0.00000000e+00,
         5.88554265e-01,  0.00000000e+00, -9.99999534e-01,
         0.00000000e+00,  5.86991651e-01,  0.00000000e+00,
         3.09963574e-01,  0.00000000e+00, -9.51368234e-01,
         0.00000000e+00,  8.08413990e-01,  0.00000000e+00,
         1.04002571e-03,  0.00000000e+00, -8.09636589e-01,
         0.00000000e+00,  9.50725404e-01,  0.00000000e+00,
        -3.07985298e-01,  0.00000000e+00, -5.88674375e-01,
         0.00000000e+00,  9.99999379e-01,  0.00000000e+00,
        -5.86871359e-01,  0.00000000e+00, -3.10104828e-01,
         0.00000000e+00,  9.51413993e-01,  0.00000000e+00,
        -8.08326528e-01,  0.00000000e+00, -1.18860075e-03,
         0.00000000e+00],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
         0.00000000e+00]]))
C_nv = sp.Matrix(np.array([[ 0.00000000e+00,  9.87684580e-01,  0.00000000e+00,
        -3.09062722e-01,  0.00000000e+00, -8.90973779e-01,
         0.00000000e+00,  5.87863046e-01,  0.00000000e+00,
         7.07021780e-01,  0.00000000e+00, -8.09101770e-01,
         0.00000000e+00, -4.53840551e-01,  0.00000000e+00,
         9.51115930e-01,  0.00000000e+00,  1.56220760e-01,
         0.00000000e+00, -9.99999971e-01,  0.00000000e+00,
         1.56695650e-01,  0.00000000e+00,  9.50967330e-01,
         0.00000000e+00, -4.54268941e-01,  0.00000000e+00,
        -8.08819119e-01,  0.00000000e+00,  7.07361723e-01,
         0.00000000e+00,  5.87474022e-01,  0.00000000e+00,
        -8.91191991e-01,  0.00000000e+00, -3.08605415e-01,
         0.00000000e+00,  9.87759692e-01,  0.00000000e+00,
        -4.80810494e-04,  0.00000000e+00, -9.87609239e-01,
         0.00000000e+00,  3.09519957e-01,  0.00000000e+00,
         8.90755362e-01,  0.00000000e+00, -5.88251935e-01,
         0.00000000e+00, -7.06681673e-01,  0.00000000e+00,
         8.09384234e-01,  0.00000000e+00,  4.53412057e-01,
         0.00000000e+00, -9.51264311e-01,  0.00000000e+00,
        -1.55745835e-01,  0.00000000e+00,  9.99999740e-01,
         0.00000000e+00, -1.57170502e-01,  0.00000000e+00,
        -9.50818509e-01,  0.00000000e+00,  4.54697226e-01,
         0.00000000e+00,  8.08536282e-01,  0.00000000e+00,
        -7.07701503e-01,  0.00000000e+00, -5.87084861e-01,
         0.00000000e+00,  8.91409996e-01,  0.00000000e+00,
         3.08148037e-01,  0.00000000e+00, -9.87834576e-01,
         0.00000000e+00,  9.61620876e-04,  0.00000000e+00,
         9.87533669e-01,  0.00000000e+00, -3.09977120e-01,
         0.00000000e+00, -8.90536739e-01,  0.00000000e+00,
         5.88640688e-01,  0.00000000e+00,  7.06341403e-01,
         0.00000000e+00, -8.09666510e-01,  0.00000000e+00,
        -4.52983458e-01,  0.00000000e+00,  9.51412472e-01,
         0.00000000e+00,  1.55270874e-01,  0.00000000e+00,
        -9.99999278e-01,  0.00000000e+00,  1.57645319e-01,
         0.00000000e+00,  9.50669469e-01,  0.00000000e+00,
        -4.55125405e-01,  0.00000000e+00, -8.08253257e-01,
         0.00000000e+00,  7.08041120e-01,  0.00000000e+00,
         5.86695565e-01,  0.00000000e+00, -8.91627795e-01,
         0.00000000e+00, -3.07690588e-01,  0.00000000e+00,
         9.87909232e-01,  0.00000000e+00, -1.44243104e-03,
         0.00000000e+00, -9.87457872e-01,  0.00000000e+00,
         3.10434212e-01,  0.00000000e+00,  8.90317910e-01,
         0.00000000e+00, -5.89029304e-01,  0.00000000e+00,
        -7.06000969e-01,  0.00000000e+00,  8.09948600e-01,
         0.00000000e+00,  4.52554754e-01,  0.00000000e+00,
        -9.51560413e-01,  0.00000000e+00, -1.54795877e-01,
         0.00000000e+00,  9.99998584e-01,  0.00000000e+00,
        -1.58120099e-01,  0.00000000e+00, -9.50520209e-01,
         0.00000000e+00,  4.55553479e-01,  0.00000000e+00,
         8.07970045e-01,  0.00000000e+00, -7.08380573e-01,
         0.00000000e+00, -5.86306133e-01,  0.00000000e+00,
         8.91845388e-01,  0.00000000e+00,  3.07233068e-01,
         0.00000000e+00, -9.87983660e-01,  0.00000000e+00,
         1.92324086e-03]]))
D11_nv = sp.Matrix(np.array([[0., 0.],
       [0., 0.]]))
D12_nv = sp.Matrix(np.array([[0. ],
       [0.5]]))
D21_nv = sp.Matrix(np.array([[0. , 1.9]]))


# ---------- 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 = []
Related Problems:
Extensive Material:
Result: Inaccurate. (Different result than expected.)
Last Build: Checkout CI Build
Runtime: 54.5 (estimated: 10s)