GUI modules

def changeValue(operating_conditions_frame, accessible_parameters_frame, undetermined_parameters_frame,
                current_density_parameters_frame, computing_parameters_frame, choice_operating_conditions,
                choice_accessible_parameters, choice_undetermined_parameters, choice_current_density_parameters,
                choice_computing_parameters, choices_buttons):
    """This function is called when the user selects a specific option from a dropdown menu for the type of fuel cell.
    Depending on the selected option, it either hides or displays specific input fields (labels or entry widgets) on
    the GUI.

    Parameters
    ----------
    operating_conditions_frame : ttk.Frame
        The frame where the graphical elements for the operating condition and the choice of fuel cell are placed.
    accessible_parameters_frame : ttk.Frame
        The frame where the graphical elements for the accessible physical parameters are placed.
    undetermined_parameters_frame : ttk.Frame
        The frame where the graphical elements for the undetermined physical parameters are placed.
    current_density_parameters_frame : ttk.Frame
        The frame where the graphical elements for the current density parameters are placed.
    computing_parameters_frame : ttk.Frame
        The frame where the graphical elements for the computing parameters are placed.
    choice_operating_conditions : dict
        A dictionary containing the operating condition information.
    choice_accessible_parameters : dict
        A dictionary containing the accessible physical parameter information.
    choice_undetermined_parameters : dict
        A dictionary containing the undetermined physical parameter information.
    choice_current_density_parameters : dict
        A dictionary containing the current density parameter information.
    choice_computing_parameters : dict
        A dictionary containing the computing parameter information.
    choices_buttons : dict
        A dictionary containing the button information.
    """

    if choices_buttons['type_fuel_cell']['value'].get() != 'Enter your specifications':
        # Recovers the new settings
        recover_for_display_operating_inputs_and_physical_parameters(choice_operating_conditions,
                                                                     choice_accessible_parameters,
                                                                     choice_undetermined_parameters,
                                                                     choice_current_density_parameters,
                                                                     choice_computing_parameters, choices_buttons)
        # Display the labels for ...
        #       operating conditions
        for k, v in choice_operating_conditions.items():
            ttk.Label(operating_conditions_frame, width=7, anchor='w', textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       accessible physical parameters
        for k, v in choice_accessible_parameters.items():
            ttk.Label(accessible_parameters_frame, width=7, anchor='w', textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       undetermined physical parameters
        for k, v in choice_undetermined_parameters.items():
            ttk.Label(undetermined_parameters_frame, width=7, anchor='w', textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       current density parameters
        for k, v in choice_current_density_parameters.items():
            ttk.Label(current_density_parameters_frame, width=7, anchor='w', textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       computing parameters
        for k, v in choice_computing_parameters.items():
            ttk.Label(computing_parameters_frame, width=7, anchor='w', textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)

    else:  # choices_buttons['type_fuel_cell']['value'].get() == 'Enter your specifications':
        # Saves and displays the user entries for ...
        #       operating conditions
        for k, v in choice_operating_conditions.items():
            ttk.Entry(operating_conditions_frame, width=7, textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       accessible physical parameters
        for k, v in choice_accessible_parameters.items():
            ttk.Entry(accessible_parameters_frame, width=7, textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       undetermined physical parameters
        for k, v in choice_undetermined_parameters.items():
            ttk.Entry(undetermined_parameters_frame, width=7, textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       current density parameters
        for k, v in choice_current_density_parameters.items():
            ttk.Entry(current_density_parameters_frame, width=7, textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)
        #       computing parameters
        for k, v in choice_computing_parameters.items():
            ttk.Entry(computing_parameters_frame, width=7, textvariable=v['value']). \
                grid(row=v['label_row'], column=v['label_column'], padx=5)

def display_parameter_labels(operating_conditions_frame, accessible_parameters_frame, undetermined_parameters_frame,
                             current_density_parameters_frame, computing_parameters_frame, choice_operating_conditions,
                             choice_accessible_parameters, choice_undetermined_parameters,
                             choice_current_density_parameters, choice_computing_parameters):
    """This function displays labels on the GUI, representing operating conditions and physical parameters, without
    their actual values.

    Parameters
    ----------
    operating_conditions_frame : ttk.Frame
        The frame where the graphical elements for the operating condition and the choice of fuel cell are placed.
    accessible_parameters_frame : ttk.Frame
        The frame where the graphical elements for the accessible physical parameters are placed.
    undetermined_parameters_frame : ttk.Frame
        The frame where the graphical elements for the undetermined physical parameters are placed.
    current_density_parameters_frame : ttk.Frame
        The frame where the graphical elements for the current density parameters are placed.
    computing_parameters_frame : ttk.Frame
        The frame where the graphical elements for the computing parameters are placed.
    choice_operating_conditions : dict
        A dictionary containing the operating condition information.
    choice_accessible_parameters : dict
        A dictionary containing the accessible physical parameter information.
    choice_undetermined_parameters : dict
        A dictionary containing the undetermined physical parameter information.
    choice_current_density_parameters : dict
        A dictionary containing the current density parameter information.
    choice_computing_parameters : dict
        A dictionary containing the computing parameter information.
    """

    # Display the titles
    ttk.Label(operating_conditions_frame, text='Operating conditions', font=('cmr10', 12, 'bold')). \
        grid(row=1, column=0, columnspan=6, ipady=15)
    ttk.Label(accessible_parameters_frame, text='Accessible physical parameters', font=('cmr10', 12, 'bold')). \
        grid(row=0, column=0, columnspan=6, ipady=15)

    # Display the labels for ...
    #       operating conditions
    for k, v in choice_operating_conditions.items():
        ttk.Label(operating_conditions_frame, text=k, font=('cmr10', 10)). \
            grid(row=v['label_row'], column=v['label_column'] - 1, sticky="w")
    #       accessible physical parameters
    for k, v in choice_accessible_parameters.items():
        ttk.Label(accessible_parameters_frame, text=k, font=('cmr10', 10)). \
            grid(row=v['label_row'], column=v['label_column'] - 1, sticky="w")
    #       undetermined physical parameters
    for k, v in choice_undetermined_parameters.items():
        ttk.Label(undetermined_parameters_frame, text=k, font=('cmr10', 10)). \
            grid(row=v['label_row'], column=v['label_column'] - 1, sticky="w")
    #       current density parameters
    for k, v in choice_current_density_parameters.items():
        ttk.Label(current_density_parameters_frame, text=k, font=('cmr10', 10)). \
            grid(row=v['label_row'], column=v['label_column'] - 1, sticky="w")
    #       computing parameters
    for k, v in choice_computing_parameters.items():
        ttk.Label(computing_parameters_frame, text=k, font=('cmr10', 10)). \
            grid(row=v['label_row'], column=v['label_column'] - 1, sticky="w")

def display_parameters_value(operating_conditions_frame, accessible_parameters_frame, undetermined_parameters_frame,
                             current_density_parameters_frame, computing_parameters_frame, choice_operating_conditions,
                             choice_accessible_parameters, choice_undetermined_parameters,
                             choice_current_density_parameters, choice_computing_parameters):
    """This function displays entry widgets on the GUI. There, the user can enter values for operating conditions and
    physical parameters.

    Parameters
    ----------
    operating_conditions_frame : ttk.Frame
        The frame where the graphical elements for the operating condition and the choice of fuel cell are placed.
    accessible_parameters_frame : ttk.Frame
        The frame where the graphical elements for the accessible physical parameters are placed.
    undetermined_parameters_frame : ttk.Frame
        The frame where the graphical elements for the undetermined physical parameters are placed.
    current_density_parameters_frame : ttk.Frame
        The frame where the graphical elements for the current density parameters are placed.
    computing_parameters_frame : ttk.Frame
        The frame where the graphical elements for the computing parameters are placed.
    choice_operating_conditions : dict
        A dictionary containing the operating condition information.
    choice_accessible_parameters : dict
        A dictionary containing the accessible physical parameter information.
    choice_undetermined_parameters : dict
        A dictionary containing the undetermined physical parameter information.
    choice_current_density_parameters : dict
        A dictionary containing the current density parameter information.
    choice_computing_parameters : dict
        A dictionary containing the computing parameter information.
    """
    # Display the value for ...
    #       operating conditions
    for k, v in choice_operating_conditions.items():
        ttk.Entry(operating_conditions_frame, width=7, textvariable=v['value']). \
            grid(row=v['label_row'], column=v['label_column'], padx=5)
    #       accessible physical parameters
    for k, v in choice_accessible_parameters.items():
        ttk.Entry(accessible_parameters_frame, width=7, textvariable=v['value']). \
            grid(row=v['label_row'], column=v['label_column'], padx=5)
    #       undetermined physical parameters
    for k, v in choice_undetermined_parameters.items():
        ttk.Entry(undetermined_parameters_frame, width=7, textvariable=v['value']). \
            grid(row=v['label_row'], column=v['label_column'], padx=5)
    #       current density parameters
    for k, v in choice_current_density_parameters.items():
        ttk.Entry(current_density_parameters_frame, width=7, textvariable=v['value']). \
            grid(row=v['label_row'], column=v['label_column'], padx=5)
    #       computing parameters
    for k, v in choice_computing_parameters.items():
        ttk.Entry(computing_parameters_frame, width=7, textvariable=v['value']). \
            grid(row=v['label_row'], column=v['label_column'], padx=5)

def display_radiobuttons(model_possibilities_frame, choices_buttons):
    """This function displays radiobuttons on the GUI, allowing the user to make choices for control, results display,
    plot style, etc.

    Parameters
    ----------
    model_possibilities_frame : ttk.Frame
        The frame where the graphical elements for the model possibilities and the choice of current density are placed.
    choices_buttons : dict
        A dictionary containing the button information.
    """

    ttk.Label(model_possibilities_frame, text='Model possibilities', font=('cmr10', 12, 'bold')) \
        .grid(row=0, column=0, columnspan=6, ipady=15)

    # Ask the user to choose an option and save it
    ttk.Label(model_possibilities_frame, text='Auxiliaries: ', font=('cmr10', 12)). \
        grid(row=choices_buttons['type_auxiliary']['label_row'], column=0, columnspan=1, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='No auxiliaries', value=0,
                    variable=choices_buttons['type_auxiliary']['value']). \
        grid(row=choices_buttons['type_auxiliary']['label_row'], column=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Forced-convective cathode\nwith anodic recirculation', value=1,
                    variable=choices_buttons['type_auxiliary']['value']). \
        grid(row=choices_buttons['type_auxiliary']['label_row'], column=3, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Forced-convective cathode\nwith flow-through anode', value=2,
                    variable=choices_buttons['type_auxiliary']['value']). \
        grid(row=choices_buttons['type_auxiliary']['label_row'], column=4, sticky="w")

    # Ask the user to choose an option and save it
    ttk.Label(model_possibilities_frame, text='Control: ', font=('cmr10', 12)). \
        grid(row=choices_buttons['type_control']['label_row'], column=0, columnspan=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='No control', value=0,
                    variable=choices_buttons['type_control']['value']). \
        grid(row=choices_buttons['type_control']['label_row'], column=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Humidity', value=1,
                    variable=choices_buttons['type_control']['value']). \
        grid(row=choices_buttons['type_control']['label_row'], column=3, sticky="w")

    # Ask the user to choose an option and save it
    ttk.Label(model_possibilities_frame, text='Purge: ', font=('cmr10', 12)). \
        grid(row=choices_buttons['type_purge']['label_row'], column=0, columnspan=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='No purge', value=0,
                    variable=choices_buttons['type_purge']['value']). \
        grid(row=choices_buttons['type_purge']['label_row'], column=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Periodic', value=1,
                    variable=choices_buttons['type_purge']['value']). \
        grid(row=choices_buttons['type_purge']['label_row'], column=3, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Constant', value=2,
                    variable=choices_buttons['type_purge']['value']). \
        grid(row=choices_buttons['type_purge']['label_row'], column=4, sticky="w")

    # Ask the user to choose an option and save it
    ttk.Label(model_possibilities_frame, text='Display: ', font=('cmr10', 12)). \
        grid(row=choices_buttons['type_display']['label_row'], column=0, columnspan=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='No display', value=0,
                    variable=choices_buttons['type_display']['value']). \
        grid(row=choices_buttons['type_display']['label_row'], column=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Synthetic', value=1,
                    variable=choices_buttons['type_display']['value']). \
        grid(row=choices_buttons['type_display']['label_row'], column=3, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Multiple', value=2,
                    variable=choices_buttons['type_display']['value']). \
        grid(row=choices_buttons['type_display']['label_row'], column=4, sticky="w")

    # Ask the user to choose an option and save it
    ttk.Label(model_possibilities_frame, text='Plot: ', font=('cmr10', 12)). \
        grid(row=choices_buttons['type_plot']['label_row'], column=0, columnspan=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Fixed', value=0,
                    variable=choices_buttons['type_plot']['value']). \
        grid(row=choices_buttons['type_plot']['label_row'], column=2, sticky="w")
    ttk.Radiobutton(model_possibilities_frame, text='Dynamic', value=1,
                    variable=choices_buttons['type_plot']['value']). \
        grid(row=choices_buttons['type_plot']['label_row'], column=3, sticky="w")

def launch_AlphaPEM_for_EIS_current(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                                    i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc,
                                    Wgc, Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co,
                                    kappa_c, a_slim, b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell,
                                    type_current, type_auxiliary, type_control, type_purge, type_display, type_plot):
    """Launch the AlphaPEM simulator for an EIS current density and display the results.

    Parameters
    ----------
    current_density : function
        Current density evolution over time (operating input). It is a function of time and parameters dictionary.
    T_des : float
        Desired fuel cell temperature in Kelvin (operating input).
    Pa_des : float
        Desired anode pressure in Pascal (operating input).
    Pc_des : float
        Desired cathode pressure in Pascal (operating input).
    Sa : float
        Stoichiometric ratio of hydrogen (operating input).
    Sc : float
        Stoichiometric ratio of oxygen (operating input).
    Phi_a_des : float
        Desired anode relative humidity (operating input).
    Phi_c_des : float
        Desired cathode relative humidity (operating input).
    t_step : tuple
        Time parameters for the step_current density function (current parameters).
        It is a tuple containing the initial time 't0_step', final time 'tf_step', loading time 'delta_t_load_step'
        and dynamic time for display 'delta_t_dyn_step'.
    i_step : tuple
        Current parameters for the step_current density function (current parameters).
        It is a tuple containing the initial and final current density value 'i_ini_step' and 'i_final_step'.
    i_max_pola : float
        Maximum current density for the polarization curve (current parameter).
    delta_pola : tuple
        Parameters for the polarization curve (current parameters). It is a tuple containing the loading time
        'delta_t_load_pola', the breaking time 'delta_t_break_pola', the current density step 'delta_i_pola', and
        the initial breaking time 'delta_t_ini_pola'.
    i_EIS : float
        Current for which a ratio_EIS perturbation is added (current parameter).
    ratio_EIS : float
        Value of the perturbation on the current density for building the EIS curve (current parameter).
    t_EIS : tuple
        EIS parameters (current parameters). It is a tuple containing the initial EIS time after stack equilibrium
        't0_EIS', a list of time parameters which gives the beginning of each frequency change 't_new_start_EIS',
        the final time 'tf_EIS', a list of time parameters which gives the estimated time for reaching equilibrium
        at each frequency 'delta_t_break_EIS', and a list of time parameters which gives the estimated time for
        measuring the voltage response at each frequency 'delta_t_measurement_EIS'.
    f_EIS : tuple
        EIS parameters (current parameters). It is a tuple containing the power of the initial frequency
        'f_power_min_EIS': f_min_EIS = 10**f_power_min_EIS, the power of the final frequency 'f_power_max_EIS', the
        number of frequencies tested 'nb_f_EIS' and the number of points calculated per specific period
        'nb_points_EIS'.
    Aact : float
        Active area of the cell in m² (accessible physical parameter).
    Hgdl : float
        Thickness of the gas diffusion layer in m (accessible physical parameter).
    Hmem : float
        Thickness of the membrane in m (accessible physical parameter).
    Hcl : float
        Thickness of the catalyst layer in m (accessible physical parameter).
    Hgc : float
        Thickness of the gas channel in m (accessible physical parameter).
    Wgc : float
        Width of the gas channel in m (accessible physical parameter).
    Lgc : float
        Length of the gas channel in m (accessible physical parameter).
    epsilon_gdl : float
        Anode/cathode GDL porosity (undetermined physical parameter).
    tau : float
        Pore structure coefficient (undetermined physical parameter).
    epsilon_mc : float
        Volume fraction of ionomer in the CL (undetermined physical parameter).
    epsilon_c : float
        Compression ratio of the GDL (undetermined physical parameter).
    e : float
        Capillary exponent (undetermined physical parameter).
    Re : float
        Electron conduction resistance of the circuit in ohm.m² (undetermined physical parameter).
    i0_c_ref : float
        Reference exchange current density at the cathode in A.m-2 (undetermined physical parameter).
    kappa_co : float
        Crossover correction coefficient in mol.m-1.s-1.Pa-1 (undetermined physical parameter).
    kappa_c : float
        Overpotential correction exponent (undetermined physical parameter).
    a_slim : float
        One of the limit liquid saturation coefficients: the slop of slim function
        (undetermined physical parameter).
    b_slim : float
        One of the limit liquid saturation coefficients: the intercept of slim function
        (undetermined physical parameter).
    a_switch : float
        One of the limit liquid saturation coefficients: the slop of s_switch function
        (undetermined physical parameter).
    C_scl : float
        Volumetric space-charge layer capacitance in F.m-3 (undetermined physical parameter).
    max_step : float
        Maximum time step for the solver (computing parameter).
    n_gdl : int
        Number of points considered in the GDL (computing parameter).
    t_purge : tuple
        Time parameters for purging the system (computing parameter).
        It is the purge time interval 'purge_time' and the time between two purges 'delta_purge'.
    type_fuel_cell : str
        Type of fuel cell configuration (computing parameter).
    type_current : str
        Type of current density function (computing parameter).
    type_auxiliary : str
        Type of auxiliary system (computing parameter).
    type_control : str
        Type of control system (computing parameter).
    type_purge : str
        Type of purge system (computing parameter).
    type_display : str
        Type of display (computing parameter).
    type_plot : str
        Type of plot (computing parameter).
    """

    # Starting time
    start_time = time.time()

    # Figures preparation
    fig1, ax1, fig2, ax2, fig3, ax3 = figures_preparation(type_current, type_display)

    # Initialization
    #       ... of the plot update number (n) and the initial time interval (time_interval)
    initial_variable_values = None
    t0_EIS, t_new_start, tf_EIS, delta_t_break_EIS, delta_t_measurement_EIS = t_EIS
    f_power_min_EIS, f_power_max_EIS, nb_f_EIS, nb_points_EIS = f_EIS  # These are used for EIS max_step
    #                                                                    actualization.
    f = np.logspace(f_power_min_EIS, f_power_max_EIS, num=nb_f_EIS)  # It is a list of all the frequency tested.
    n = len(t_new_start)  # It is the plot update number.
    time_interval = [0, t0_EIS]  # It is the initial time interval.

    #       A preliminary simulation run is necessary to equilibrate the internal variables of the cell at i_EIS
    #       prior to initiating the EIS.
    Simulator = AlphaPEM(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                         i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc, Wgc,
                         Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co, kappa_c, a_slim,
                         b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell, type_current,
                         type_auxiliary, type_control, type_purge, type_display, type_plot,
                         initial_variable_values, time_interval)

    # time_interval actualization
    t0_EIS_temp = t0_EIS  # It is the initial time for 1 EIS point.
    tf_EIS_temp = t_new_start[0] + delta_t_break_EIS[0] + delta_t_measurement_EIS[0]  # It is the final time for
    #                                                                                  1 EIS point.
    n_inf = np.where(t_new_start <= t0_EIS_temp)[0][-1]  # It is the number of frequency changes which has been
    #                                                      made.
    max_step = 1 / (f[n_inf] * nb_points_EIS)  # max_step is actualized according to the current frequency
    #                                        for increased calculation
    time_interval = [t0_EIS_temp, tf_EIS_temp]

    # Recovery of the internal states from the end of the preceding simulation.
    initial_variable_values = []
    for x in Simulator.solver_variable_names:
        initial_variable_values.append(Simulator.variables[x][-1])

    # Dynamic simulation
    for i in range(n):
        Simulator = AlphaPEM(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                             i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc,
                             Wgc, Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co,
                             kappa_c, a_slim, b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell,
                             type_current, type_auxiliary, type_control, type_purge, type_display, type_plot,
                             initial_variable_values, time_interval)

        # time_interval actualization
        if i < (n - 1):  # The final simulation does not require actualization.
            t0_EIS_temp = Simulator.variables['t'][-1]  # It is the initial time for 1 EIS point.
            tf_EIS_temp = t_new_start[i + 1] + delta_t_break_EIS[i + 1] + delta_t_measurement_EIS[i + 1]  # It
            #                                                                 is the final time for 1 EIS point.
            n_inf = np.where(t_new_start <= t0_EIS_temp)[0][-1]  # It is the number of frequency changes which
            #                                                      has been made.
            max_step = 1 / (f[n_inf] * nb_points_EIS)  # max_step is actualized according to the current
            #                                            frequency for increased calculation
            time_interval = [t0_EIS_temp, tf_EIS_temp]  # It is the time interval for 1 EIS point.

        # Recovery of the internal states from the end of the preceding simulation.
        initial_variable_values = []
        for x in Simulator.solver_variable_names:
            initial_variable_values.append(Simulator.variables[x][-1])

        # Display
        if type_display != "no_display":
            Simulator.Display(ax1, ax2, ax3)

    # Plot saving
    plot_saving(type_fuel_cell, type_current, type_display, fig1, fig2, fig3)

    # Ending time
    algo_time = time.time() - start_time
    print('Time of the algorithm in second :', algo_time)

def launch_AlphaPEM_for_polarization_current(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step,
                                             i_step, i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl,
                                             Hmem, Hcl, Hgc, Wgc, Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re,
                                             i0_c_ref, kappa_co, kappa_c, a_slim, b_slim, a_switch, C_scl, max_step,
                                             n_gdl, t_purge, type_fuel_cell, type_current, type_auxiliary, type_control,
                                             type_purge, type_display, type_plot):
    """Launch the AlphaPEM simulator for a polarization current density and display the results.

    Parameters
    ----------
    current_density : function
        Current density evolution over time (operating input). It is a function of time and parameters dictionary.
    T_des : float
        Desired fuel cell temperature in Kelvin (operating input).
    Pa_des : float
        Desired anode pressure in Pascal (operating input).
    Pc_des : float
        Desired cathode pressure in Pascal (operating input).
    Sa : float
        Stoichiometric ratio of hydrogen (operating input).
    Sc : float
        Stoichiometric ratio of oxygen (operating input).
    Phi_a_des : float
        Desired anode relative humidity (operating input).
    Phi_c_des : float
        Desired cathode relative humidity (operating input).
    t_step : tuple
        Time parameters for the step_current density function (current parameters).
        It is a tuple containing the initial time 't0_step', final time 'tf_step', loading time 'delta_t_load_step'
        and dynamic time for display 'delta_t_dyn_step'.
    i_step : tuple
        Current parameters for the step_current density function (current parameters).
        It is a tuple containing the initial and final current density value 'i_ini_step' and 'i_final_step'.
    i_max_pola : float
        Maximum current density for the polarization curve (current parameter).
    delta_pola : tuple
        Parameters for the polarization curve (current parameters). It is a tuple containing the loading time
        'delta_t_load_pola', the breaking time 'delta_t_break_pola', the current density step 'delta_i_pola', and
        the initial breaking time 'delta_t_ini_pola'.
    i_EIS : float
        Current for which a ratio_EIS perturbation is added (current parameter).
    ratio_EIS : float
        Value of the perturbation on the current density for building the EIS curve (current parameter).
    t_EIS : tuple
        EIS parameters (current parameters). It is a tuple containing the initial EIS time after stack equilibrium
        't0_EIS', a list of time parameters which gives the beginning of each frequency change 't_new_start_EIS',
        the final time 'tf_EIS', a list of time parameters which gives the estimated time for reaching equilibrium
        at each frequency 'delta_t_break_EIS', and a list of time parameters which gives the estimated time for
        measuring the voltage response at each frequency 'delta_t_measurement_EIS'.
    f_EIS : tuple
        EIS parameters (current parameters). It is a tuple containing the power of the initial frequency
        'f_power_min_EIS': f_min_EIS = 10**f_power_min_EIS, the power of the final frequency 'f_power_max_EIS', the
        number of frequencies tested 'nb_f_EIS' and the number of points calculated per specific period
        'nb_points_EIS'.
    Aact : float
        Active area of the cell in m² (accessible physical parameter).
    Hgdl : float
        Thickness of the gas diffusion layer in m (accessible physical parameter).
    Hmem : float
        Thickness of the membrane in m (accessible physical parameter).
    Hcl : float
        Thickness of the catalyst layer in m (accessible physical parameter).
    Hgc : float
        Thickness of the gas channel in m (accessible physical parameter).
    Wgc : float
        Width of the gas channel in m (accessible physical parameter).
    Lgc : float
        Length of the gas channel in m (accessible physical parameter).
    epsilon_gdl : float
        Anode/cathode GDL porosity (undetermined physical parameter).
    tau : float
        Pore structure coefficient (undetermined physical parameter).
    epsilon_mc : float
        Volume fraction of ionomer in the CL (undetermined physical parameter).
    epsilon_c : float
        Compression ratio of the GDL (undetermined physical parameter).
    e : float
        Capillary exponent (undetermined physical parameter).
    Re : float
        Electron conduction resistance of the circuit in ohm.m² (undetermined physical parameter).
    i0_c_ref : float
        Reference exchange current density at the cathode in A.m-2 (undetermined physical parameter).
    kappa_co : float
        Crossover correction coefficient in mol.m-1.s-1.Pa-1 (undetermined physical parameter).
    kappa_c : float
        Overpotential correction exponent (undetermined physical parameter).
    a_slim : float
        One of the limit liquid saturation coefficients: the slop of slim function
        (undetermined physical parameter).
    b_slim : float
        One of the limit liquid saturation coefficients: the intercept of slim function
        (undetermined physical parameter).
    a_switch : float
        One of the limit liquid saturation coefficients: the slop of s_switch function
        (undetermined physical parameter).
    C_scl : float
        Volumetric space-charge layer capacitance in F.m-3 (undetermined physical parameter).
    max_step : float
        Maximum time step for the solver (computing parameter).
    n_gdl : int
        Number of points considered in the GDL (computing parameter).
    t_purge : tuple
        Time parameters for purging the system (computing parameter).
        It is the purge time interval 'purge_time' and the time between two purges 'delta_purge'.
    type_fuel_cell : str
        Type of fuel cell configuration (computing parameter).
    type_current : str
        Type of current density function (computing parameter).
    type_auxiliary : str
        Type of auxiliary system (computing parameter).
    type_control : str
        Type of control system (computing parameter).
    type_purge : str
        Type of purge system (computing parameter).
    type_display : str
        Type of display (computing parameter).
    type_plot : str
        Type of plot (computing parameter).
    """

    # Starting time
    start_time = time.time()

    # Figures preparation
    fig1, ax1, fig2, ax2, fig3, ax3 = figures_preparation(type_current, type_display)

    # Dynamic display requires a dedicated use of the AlphaPEM class.
    if type_plot == "dynamic":
        # Initialization
        #       ... of the plot update number (n) and the initial time interval (time_interval)
        initial_variable_values = None
        delta_t_load_pola, delta_t_break_pola, delta_i_pola, delta_t_ini_pola = delta_pola
        delta_t = delta_t_load_pola + delta_t_break_pola  # s. It is the time of one load.
        tf = delta_t_ini_pola + int(i_max_pola_1 / delta_i_pola + 1) * delta_t  # s. It is the polarization current
        #                                                                            duration.
        n = int(tf / delta_t)  # It is the plot update number.
        time_interval = [0, delta_t_ini_pola + delta_t]  # It is the initial time interval.

        # Dynamic simulation
        for i in range(n):
            Simulator = AlphaPEM(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                                 i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc,
                                 Wgc, Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co, kappa_c,
                                 a_slim, b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell, type_current,
                                 type_auxiliary, type_control, type_purge, type_display, type_plot,
                                 initial_variable_values, time_interval)

            # time_interval actualization
            if i < (n - 1):  # The final simulation does not require actualization.
                t0_interval = Simulator.variables['t'][-1]
                tf_interval = delta_t_ini_pola + (i + 2) * delta_t
                time_interval = [t0_interval, tf_interval]  # Reset of the time interval

            # Recovery of the internal states from the end of the preceding simulation.
            initial_variable_values = []
            for x in Simulator.solver_variable_names:
                initial_variable_values.append(Simulator.variables[x][-1])

            # Display
            if type_display != "no_display":
                Simulator.Display(ax1, ax2, ax3)

    else:  # elif type_plot == "fixed":
        # Simulation
        Simulator = AlphaPEM(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                             i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc, Wgc,
                             Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co, kappa_c, a_slim,
                             b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell, type_current,
                             type_auxiliary, type_control, type_purge, type_display, type_plot)
        # Display
        if type_display != "no_display":
            Simulator.Display(ax1, ax2, ax3)

    # Plot saving
    plot_saving(type_fuel_cell, type_current, type_display, fig1, fig2, fig3)

    # Ending time
    algo_time = time.time() - start_time
    print('Time of the algorithm in second :', algo_time)

def launch_AlphaPEM_for_step_current(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                                     i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc,
                                     Wgc, Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co,
                                     kappa_c, a_slim, b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell,
                                     type_current, type_auxiliary, type_control, type_purge, type_display, type_plot):
    """Launch the AlphaPEM simulator for a step current density and display the results.

    Parameters
    ----------
    current_density : function
        Current density evolution over time (operating input). It is a function of time and parameters dictionary.
    T_des : float
        Desired fuel cell temperature in Kelvin (operating input).
    Pa_des : float
        Desired anode pressure in Pascal (operating input).
    Pc_des : float
        Desired cathode pressure in Pascal (operating input).
    Sa : float
        Stoichiometric ratio of hydrogen (operating input).
    Sc : float
        Stoichiometric ratio of oxygen (operating input).
    Phi_a_des : float
        Desired anode relative humidity (operating input).
    Phi_c_des : float
        Desired cathode relative humidity (operating input).
    t_step : tuple
        Time parameters for the step_current density function (current parameters).
        It is a tuple containing the initial time 't0_step', final time 'tf_step', loading time 'delta_t_load_step'
        and dynamic time for display 'delta_t_dyn_step'.
    i_step : tuple
        Current parameters for the step_current density function (current parameters).
        It is a tuple containing the initial and final current density value 'i_ini_step' and 'i_final_step'.
    i_max_pola : float
        Maximum current density for the polarization curve (current parameter).
    delta_pola : tuple
        Parameters for the polarization curve (current parameters). It is a tuple containing the loading time
        'delta_t_load_pola', the breaking time 'delta_t_break_pola', the current density step 'delta_i_pola', and
        the initial breaking time 'delta_t_ini_pola'.
    i_EIS : float
        Current for which a ratio_EIS perturbation is added (current parameter).
    ratio_EIS : float
        Value of the perturbation on the current density for building the EIS curve (current parameter).
    t_EIS : tuple
        EIS parameters (current parameters). It is a tuple containing the initial EIS time after stack equilibrium
        't0_EIS', a list of time parameters which gives the beginning of each frequency change 't_new_start_EIS',
        the final time 'tf_EIS', a list of time parameters which gives the estimated time for reaching equilibrium
        at each frequency 'delta_t_break_EIS', and a list of time parameters which gives the estimated time for
        measuring the voltage response at each frequency 'delta_t_measurement_EIS'.
    f_EIS : tuple
        EIS parameters (current parameters). It is a tuple containing the power of the initial frequency
        'f_power_min_EIS': f_min_EIS = 10**f_power_min_EIS, the power of the final frequency 'f_power_max_EIS', the
        number of frequencies tested 'nb_f_EIS' and the number of points calculated per specific period
        'nb_points_EIS'.
    Aact : float
        Active area of the cell in m² (accessible physical parameter).
    Hgdl : float
        Thickness of the gas diffusion layer in m (accessible physical parameter).
    Hmem : float
        Thickness of the membrane in m (accessible physical parameter).
    Hcl : float
        Thickness of the catalyst layer in m (accessible physical parameter).
    Hgc : float
        Thickness of the gas channel in m (accessible physical parameter).
    Wgc : float
        Width of the gas channel in m (accessible physical parameter).
    Lgc : float
        Length of the gas channel in m (accessible physical parameter).
    epsilon_gdl : float
        Anode/cathode GDL porosity (undetermined physical parameter).
    tau : float
        Pore structure coefficient (undetermined physical parameter).
    epsilon_mc : float
        Volume fraction of ionomer in the CL (undetermined physical parameter).
    epsilon_c : float
        Compression ratio of the GDL (undetermined physical parameter).
    e : float
        Capillary exponent (undetermined physical parameter).
    Re : float
        Electron conduction resistance of the circuit in ohm.m² (undetermined physical parameter).
    i0_c_ref : float
        Reference exchange current density at the cathode in A.m-2 (undetermined physical parameter).
    kappa_co : float
        Crossover correction coefficient in mol.m-1.s-1.Pa-1 (undetermined physical parameter).
    kappa_c : float
        Overpotential correction exponent (undetermined physical parameter).
    a_slim : float
        One of the limit liquid saturation coefficients: the slop of slim function
        (undetermined physical parameter).
    b_slim : float
        One of the limit liquid saturation coefficients: the intercept of slim function
        (undetermined physical parameter).
    a_switch : float
        One of the limit liquid saturation coefficients: the slop of s_switch function
        (undetermined physical parameter).
    C_scl : float
        Volumetric space-charge layer capacitance in F.m-3 (undetermined physical parameter).
    max_step : float
        Maximum time step for the solver (computing parameter).
    n_gdl : int
        Number of points considered in the GDL (computing parameter).
    t_purge : tuple
        Time parameters for purging the system (computing parameter).
        It is the purge time interval 'purge_time' and the time between two purges 'delta_purge'.
    type_fuel_cell : str
        Type of fuel cell configuration (computing parameter).
    type_current : str
        Type of current density function (computing parameter).
    type_auxiliary : str
        Type of auxiliary system (computing parameter).
    type_control : str
        Type of control system (computing parameter).
    type_purge : str
        Type of purge system (computing parameter).
    type_display : str
        Type of display (computing parameter).
    type_plot : str
        Type of plot (computing parameter).
    """

    # Starting time
    start_time = time.time()

    # Figures preparation
    fig1, ax1, fig2, ax2, fig3, ax3 = figures_preparation(type_current, type_display)

    # Dynamic display requires a dedicated use of the AlphaPEM class.
    if type_plot == "dynamic":
        # Initialization
        #       ... of the plot update number (n) and the initial time interval (time_interval)
        initial_variable_values = None
        t0_step, tf_step, delta_t_load_step, delta_t_dyn_step = t_step
        n = int(tf_step / delta_t_dyn_step)  # It is the plot update number.
        time_interval = [0, delta_t_dyn_step]  # It is the initial time interval.

        # Dynamic simulation
        for i in range(n):
            Simulator = AlphaPEM(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                                 i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc,
                                 Wgc, Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co, kappa_c,
                                 a_slim, b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell, type_current,
                                 type_auxiliary, type_control, type_purge, type_display, type_plot,
                                 initial_variable_values, time_interval)

            # time_interval actualization
            if i < (n - 1):  # The final simulation does not require actualization.
                t0_interval = Simulator.variables['t'][-1]
                tf_interval = (i + 2) * delta_t_dyn_step
                time_interval = [t0_interval, tf_interval]  # Reset of the time interval

            # Recovery of the internal states from the end of the preceding simulation.
            initial_variable_values = []
            for x in Simulator.solver_variable_names:
                initial_variable_values.append(Simulator.variables[x][-1])

            # Display
            if type_display != "no_display":
                Simulator.Display(ax1, ax2, ax3)

    else:  # elif type_plot == "fixed":
        # Simulation
        Simulator = AlphaPEM(current_density, T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, t_step, i_step,
                             i_max_pola, delta_pola, i_EIS, ratio_EIS, t_EIS, f_EIS, Aact, Hgdl, Hmem, Hcl, Hgc, Wgc,
                             Lgc, epsilon_gdl, tau, epsilon_mc, epsilon_c, e, Re, i0_c_ref, kappa_co, kappa_c, a_slim,
                             b_slim, a_switch, C_scl, max_step, n_gdl, t_purge, type_fuel_cell, type_current,
                             type_auxiliary, type_control, type_purge, type_display, type_plot)
        # Display
        if type_display != "no_display":
            Simulator.Display(ax1, ax2, ax3)

    # Plot saving
    plot_saving(type_fuel_cell, type_current, type_display, fig1, fig2, fig3)

    # Ending time
    algo_time = time.time() - start_time
    print('Time of the algorithm in second :', algo_time)

def recover_for_display_operating_inputs_and_physical_parameters(choice_operating_conditions,
                                                                 choice_accessible_parameters,
                                                                 choice_undetermined_parameters,
                                                                 choice_current_density_parameters,
                                                                 choice_computing_parameters, choice_buttons):
    """This function retrieves parameter values for predefined stacks (e.g., "EH-31 1.5 bar (2021)", "Biao Xie 1.0 bar
    (2015)", etc.) and converts them to appropriate units for display on the GUI.

    Parameters
    ----------
    choice_operating_conditions : dict
        A dictionary containing the operating condition information.
    choice_accessible_parameters : dict
        A dictionary containing the accessible physical parameter information.
    choice_undetermined_parameters : dict
        A dictionary containing the undetermined physical parameter information.
    choice_current_density_parameters : dict
        A dictionary containing the current density parameter information.
    choice_computing_parameters : dict
        A dictionary containing the computing parameter information.
    choice_buttons : dict
        A dictionary containing the button information.
    """

    if choice_buttons['type_fuel_cell']['value'].get() == "EH-31 1.5 bar (2021)":
        type_fuel_cell = "EH-31_1.5"
    elif choice_buttons['type_fuel_cell']['value'].get() == "EH-31 2.0 bar (2021)":
        type_fuel_cell = "EH-31_2.0"
    elif choice_buttons['type_fuel_cell']['value'].get() == "EH-31 2.25 bar (2021)":
        type_fuel_cell = "EH-31_2.25"
    elif choice_buttons['type_fuel_cell']['value'].get() == "EH-31 2.5 bar (2021)":
        type_fuel_cell = "EH-31_2.5"
    elif choice_buttons['type_fuel_cell']['value'].get() == "Linhao Fan (2010)":
        type_fuel_cell = "LF"

    T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, i_max_pola = stored_operating_inputs(type_fuel_cell)

    Hcl, epsilon_mc, tau, Hmem, Hgdl, epsilon_gdl, epsilon_c, Hgc, Wgc, Lgc, Aact, e, Re, i0_c_ref, kappa_co, kappa_c, \
        a_slim, b_slim, a_switch, C_scl = \
        stored_physical_parameters(type_fuel_cell)

    # operating conditions recovery
    choice_operating_conditions['Temperature - Tfc (°C)']['value'].set(round(T_des - 273.15))  # °C
    choice_operating_conditions['Anode pressure - Pa (bar)']['value'].set(round(Pa_des / 1e5, 2))  # bar
    choice_operating_conditions['Cathode pressure - Pc (bar)']['value'].set(round(Pc_des / 1e5, 2))  # bar
    choice_operating_conditions['Anode stoichiometry - Sa']['value'].set(round(Sa, 1))
    choice_operating_conditions['Cathode stoichiometry - Sc']['value'].set(round(Sc, 1))
    choice_operating_conditions['Anode humidity - Φa']['value'].set(round(Phi_a_des, 1))
    choice_operating_conditions['Cathode humidity - Φc']['value'].set(round(Phi_c_des, 1))
    # accessible physical parameters recovery
    choice_accessible_parameters['Active area - Aact (cm²)']['value'].set(round(Aact * 1e4))  # cm²
    choice_accessible_parameters['GDL thickness - Hgdl (µm)']['value'].set(round(Hgdl * 1e6))  # µm
    choice_accessible_parameters['CL thickness - Hcl (µm)']['value'].set(round(Hcl * 1e6))  # µm
    choice_accessible_parameters['Membrane thickness - Hmem (µm)']['value'].set(round(Hmem * 1e6))  # µm
    choice_accessible_parameters['GC thickness - Hgc (µm)']['value'].set(round(Hgc * 1e6))  # µm
    choice_accessible_parameters['GC width - Wgc (µm)']['value'].set(round(Wgc * 1e6))  # µm
    choice_accessible_parameters['GC cumulated length - Lgc (m)']['value'].set(round(Lgc, 2))  # µm
    # undetermined physical parameters recovery
    choice_undetermined_parameters['GDL porosity - ε_gdl']['value'].set(round(epsilon_gdl, 3))
    choice_undetermined_parameters['Ionomer volume fraction\n- ε_mc']['value'].set(round(epsilon_mc, 3))
    choice_undetermined_parameters['Tortuosity - τ']['value'].set(round(tau, 3))
    choice_undetermined_parameters['Compression ratio - ε_c']['value'].set(round(epsilon_c, 3))
    choice_undetermined_parameters['Capillary exponent - e']['value'].set(e)
    choice_undetermined_parameters['Electron resistance\n- Re (µΩ.m²)']['value'].set(round(Re * 1e6, 2))  # µΩ.m²
    choice_undetermined_parameters['Reference exchange\ncurrent density\n- i0_c_ref (A/m²)']['value'].set(round(i0_c_ref, 2))  # A.m-2
    choice_undetermined_parameters['Crossover correction\ncoefficient\n- κ_co (mol/(m.s.Pa))']['value'].set(round(kappa_co, 2))  # mol.m-1.s-1.Pa-1
    choice_undetermined_parameters['Overpotential correction\nexponent - κ_c']['value'].set(round(kappa_c, 2))
    choice_undetermined_parameters['Limit liquid saturation\ncoefficient - a_slim']['value'].set(round(a_slim, 7))
    choice_undetermined_parameters['Limit liquid saturation\ncoefficient - b_slim']['value'].set(round(b_slim, 7))
    choice_undetermined_parameters['Limit liquid saturation\ncoefficient - a_switch']['value'].set(round(a_switch, 7))
    choice_undetermined_parameters['Volumetric space-charge\nlayer capacitance\n- C_scl (F/cm³)']['value'].set(round(C_scl * 1e-6, 2))  # F.cm-3
    # i_max_pola recovery
    choice_current_density_parameters['Maximum current density\n- i_max_pola (A/cm²)']['value'].set(round(i_max_pola / 1e4, 2))  # A/cm²

def recover_for_use_operating_inputs_and_physical_parameters(choice_operating_conditions, choice_accessible_parameters,
                                                             choice_undetermined_parameters,
                                                             choice_current_density_parameters,
                                                             choice_computing_parameters, choice_buttons):
    """This function retrieves and converts the parameter values from the GUI into standard units for further
    calculations.

    Parameters
    ----------
    choice_operating_conditions : dict
        A dictionary containing the operating condition information.
    choice_accessible_parameters : dict
        A dictionary containing the accessible physical parameter information.
    choice_undetermined_parameters : dict
        A dictionary containing the undetermined physical parameter information.
    choice_current_density_parameters : dict
        A dictionary containing the current density parameter information.
    choice_computing_parameters : dict
        A dictionary containing the computing parameter information.
    choice_buttons : dict
        A dictionary containing the button information.
    """
    # operating conditions
    T_des = choice_operating_conditions['Temperature - Tfc (°C)']['value'].get() + 273.15  # K
    Pa_des = choice_operating_conditions['Anode pressure - Pa (bar)']['value'].get() * 1e5  # Pa
    Pc_des = choice_operating_conditions['Cathode pressure - Pc (bar)']['value'].get() * 1e5  # Pa
    Sa = choice_operating_conditions['Anode stoichiometry - Sa']['value'].get()
    Sc = choice_operating_conditions['Cathode stoichiometry - Sc']['value'].get()
    Phi_a_des = choice_operating_conditions['Anode humidity - Φa']['value'].get()
    Phi_c_des = choice_operating_conditions['Cathode humidity - Φc']['value'].get()
    # accessible physical parameters
    Aact = choice_accessible_parameters['Active area - Aact (cm²)']['value'].get() * 1e-4  # m²
    Hgdl = choice_accessible_parameters['GDL thickness - Hgdl (µm)']['value'].get() * 1e-6  # m
    Hcl = choice_accessible_parameters['CL thickness - Hcl (µm)']['value'].get() * 1e-6  # m
    Hmem = choice_accessible_parameters['Membrane thickness - Hmem (µm)']['value'].get() * 1e-6  # m
    Hgc = choice_accessible_parameters['GC thickness - Hgc (µm)']['value'].get() * 1e-6  # m
    Wgc = choice_accessible_parameters['GC width - Wgc (µm)']['value'].get() * 1e-6  # m
    Lgc = choice_accessible_parameters['GC cumulated length - Lgc (m)']['value'].get()  # m
    # undetermined physical parameters
    epsilon_gdl = choice_undetermined_parameters['GDL porosity - ε_gdl']['value'].get()
    epsilon_mc = choice_undetermined_parameters['Ionomer volume fraction\n- ε_mc']['value'].get()
    tau = choice_undetermined_parameters['Tortuosity - τ']['value'].get()
    epsilon_c = choice_undetermined_parameters['Compression ratio - ε_c']['value'].get()
    e = choice_undetermined_parameters['Capillary exponent - e']['value'].get()
    Re = choice_undetermined_parameters['Electron resistance\n- Re (µΩ.m²)']['value'].get() * 1e-6  # ohm.m²
    i0_c_ref = choice_undetermined_parameters['Reference exchange\ncurrent density\n- i0_c_ref (A/m²)']['value'].get()  # A.m-2
    kappa_co = choice_undetermined_parameters['Crossover correction\ncoefficient\n- κ_co (mol/(m.s.Pa))']['value'].get()  # mol.m-1.s-1.Pa-1
    kappa_c = choice_undetermined_parameters['Overpotential correction\nexponent - κ_c']['value'].get()
    a_slim = choice_undetermined_parameters['Limit liquid saturation\ncoefficient - a_slim']['value'].get()
    b_slim = choice_undetermined_parameters['Limit liquid saturation\ncoefficient - b_slim']['value'].get()
    a_switch = choice_undetermined_parameters['Limit liquid saturation\ncoefficient - a_switch']['value'].get()
    C_scl = choice_undetermined_parameters['Volumetric space-charge\nlayer capacitance\n- C_scl (F/cm³)']['value'].get() * 1e6  # F.m-3
    # current density parameters
    t_step = (choice_current_density_parameters['Initial time - t0_step (s)']['value'].get(),
              choice_current_density_parameters['Final time - tf_step (s)']['value'].get(),
              choice_current_density_parameters['Loading time\n- Δt_load_step (s)']['value'].get(),
              choice_computing_parameters['Time for dynamic\ndisplay - Δt_dyn_step (s)']['value'].get())  # (s, s, s, s)
    i_step = (choice_current_density_parameters['Initial current density\n- i_ini_step (A/cm²)']['value'].get() * 1e4,
              choice_current_density_parameters['Final current density\n- i_final_step (A/cm²)']['value'].get() * 1e4)  # (A.m-2, A.m-2)
    i_max_pola = choice_current_density_parameters['Maximum current density\n- i_max_pola (A/cm²)']['value'].get() * 1e4  # A.m-2
    delta_pola = (choice_current_density_parameters['Loading time\n- Δt_load_pola (s)']['value'].get(),
                  choice_current_density_parameters['Breaking time\n- Δt_break_pola (s)']['value'].get(),
                  choice_current_density_parameters['Current density step\n- Δi_pola (A/cm²)']['value'].get() * 1e4,
                  choice_current_density_parameters['Initial breaking time\n- Δt_ini_pola (s)']['value'].get())  # (s, s, A.m-2, s)
    i_EIS = choice_current_density_parameters['Static current\n- i_EIS (A/cm²)']['value'].get() * 1e4  # (A.m-2)
    ratio_EIS = choice_current_density_parameters['Current ratio\n- ratio_EIS (%)']['value'].get() / 100
    f_EIS = (choice_current_density_parameters['Power of the\ninitial frequency\n- f_power_min_EIS']['value'].get(),
             choice_current_density_parameters['Power of the\nfinal frequency\n- f_power_max_EIS']['value'].get(),
             choice_current_density_parameters['Number of frequencies\ntested - nb_f_EIS']['value'].get(),
             choice_current_density_parameters['Number of points\ncalculated - nb_points_EIS']['value'].get())
    t_EIS = EIS_parameters(f_EIS)  # Time parameters for the EIS_current density function.
    t_purge = choice_computing_parameters['Purge time - t_purge (s)']['value'].get()  # s
    delta_t_purge = choice_computing_parameters['Time between two purges\n- Δt_purge (s)']['value'].get()  # s
    max_step = choice_computing_parameters['Maximum time step\n- max_step (s)']['value'].get()  # s
    n_gdl = choice_computing_parameters['Number of GDL nodes - n_gdl']['value'].get()

    if choice_buttons['type_fuel_cell']['value'].get() == "EH-31 1.5 bar (2021)":
        type_fuel_cell = "EH-31_1.5"
    elif choice_buttons['type_fuel_cell']['value'].get() == "EH-31 2.0 bar (2021)":
        type_fuel_cell = "EH-31_2.0"
    elif choice_buttons['type_fuel_cell']['value'].get() == "EH-31 2.25 bar (2021)":
        type_fuel_cell = "EH-31_2.25"
    elif choice_buttons['type_fuel_cell']['value'].get() == "EH-31 2.5 bar (2021)":
        type_fuel_cell = "EH-31_2.5"
    elif choice_buttons['type_fuel_cell']['value'].get() == "Linhao Fan (2010)":
        type_fuel_cell = "LF"
    elif choice_buttons['type_fuel_cell']['value'].get() == "Enter your specifications":
        type_fuel_cell = "manual_setup"

    if choice_buttons['type_auxiliary']['value'].get() == 0:
        type_auxiliary = "no_auxiliary"
    elif choice_buttons['type_auxiliary']['value'].get() == 1:
        type_auxiliary = "forced-convective_cathode_with_anodic_recirculation"
    else:
        type_auxiliary = "forced-convective_cathode_with_flow-through_anode"

    if choice_buttons['type_control']['value'].get() == 0:
        type_control = "no_control"
    else:
        type_control = "Phi_des"

    if choice_buttons['type_purge']['value'].get() == 0:
        type_purge = "no_purge"
    elif choice_buttons['type_purge']['value'].get() == 1:
        type_purge = "periodic_purge"
    else:
        type_purge = "constant_purge"

    if choice_buttons['type_display']['value'].get() == 0:
        type_display = "no_display"
    elif choice_buttons['type_display']['value'].get() == 1:
        type_display = "synthetic"
    else:
        type_display = "multiple"

    if choice_buttons['type_plot']['value'].get() == 0:
        type_plot = "fixed"
    else:
        type_plot = "dynamic"

    return (T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, Aact, Hgdl, Hcl, Hmem, Hgc, Wgc, Lgc, epsilon_gdl,
            epsilon_mc, tau, epsilon_c, e, Re, i0_c_ref, kappa_co, kappa_c, a_slim, b_slim, a_switch, C_scl, t_step,
            i_step, i_max_pola, delta_pola, i_EIS, ratio_EIS, f_EIS, t_EIS, t_purge, delta_t_purge, max_step, n_gdl,
            type_fuel_cell, type_auxiliary, type_control, type_purge, type_display, type_plot)