How to use the lmfit.lineshapes.lorentzian function in lmfit

def residual(pars, x, sigma=None, data=None):
        """Define objective function."""
        yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
        yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])

        model = yg + yl + pars['line_off'] + x * pars['line_slope']

        if data is None:
            return model
        if sigma is None:
            return model - data
        return (model-data) / sigma

model =  yg +  yl + pars['line_off'] + x * pars['line_slope']
        if data is None:
            return model
        if sigma is None:
            return (model - data)
        return (model - data) / sigma


    n = 201
    xmin = 0.
    xmax = 20.0
    x = linspace(xmin, xmax, n)

    data = (gaussian(x, 21, 8.1, 1.2) +
            lorentzian(x, 10, 9.6, 2.4) +
            random.normal(scale=0.23,  size=n) +
            x*0.5)

    pfit = Parameters()
    pfit.add(name='amp_g',  value=10)
    pfit.add(name='cen_g',  value=9)
    pfit.add(name='wid_g',  value=1)

    pfit.add(name='amp_tot',  value=20)
    pfit.add(name='amp_l',  expr='amp_tot - amp_g')
    pfit.add(name='cen_l',  expr='1.5+cen_g')
    pfit.add(name='wid_l',  expr='2*wid_g')

    pfit.add(name='line_slope', value=0.0)
    pfit.add(name='line_off', value=0.0)

def residual(pars, x, sigma=None, data=None):
        yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
        yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])

        model =  yg +  yl + pars['line_off'] + x * pars['line_slope']
        if data is None:
            return model
        if sigma is None:
            return (model - data)
        return (model - data) / sigma

except ImportError:
    HASPYLAB = False


def residual(pars, x, data):
    model = (gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g']) +
             lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l']))
    return model - data


n = 601
random.seed(0)
x = linspace(0, 20.0, n)

data = (gaussian(x, 21, 6.1, 1.2) +
        lorentzian(x, 10, 9.6, 1.3) +
        random.normal(scale=0.1, size=n))

pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='amp_l', value=10)
pfit.add(name='cen_g', value=5)
pfit.add(name='peak_split', value=2.5, min=0, max=5, vary=True)
pfit.add(name='cen_l', expr='peak_split+cen_g')
pfit.add(name='wid_g', value=1)
pfit.add(name='wid_l', expr='wid_g')

mini = Minimizer(residual, pfit, fcn_args=(x, data))
out = mini.leastsq()

report_fit(out.params)

out = mod.fit(yn, pars, x=xs)
    out2 = mod.fit(yn, pars, x=xs, fit_kws={'Dfun': dfunc_gaussian,
                                            'col_deriv': 1})
    print('lmfit without dfunc **************')
    print('number of function calls: ', out.nfev)
    print('params', out.best_values)
    print('lmfit with dfunc *****************')
    print('number of function calls: ', out2.nfev)
    print('params', out2.best_values)
    print('\n \n')
    out2.plot(datafmt='.')

    print('**********************************')
    print('***** Test Lorentzian ************')
    print('**********************************')
    ys = lorentzian(xs, 2.5, 0, 0.5)
    yn = ys + 0.1*np.random.normal(size=len(xs))

    mod = LorentzianModel()
    pars = mod.guess(yn, xs)
    out = mod.fit(yn, pars, x=xs)
    out2 = mod.fit(yn, pars, x=xs, fit_kws={'Dfun': dfunc_lorentzian, 'col_deriv': 1})
    print('lmfit without dfunc **************')
    print('number of function calls: ', out.nfev)
    print('params', out.best_values)
    print('lmfit with dfunc *****************')
    print('number of function calls: ', out2.nfev)
    print('params', out2.best_values)
    print('\n \n')
    out2.plot(datafmt='.')

    plt.show()

def residual(pars, x, data):
    model = (gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g']) +
             lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l']))
    return model - data

slope = pars['line_slope']
    offset = pars['line_off']
    model = yg + yl + offset + x*slope

    if data is None:
        return model
    if sigma is None:
        return model - data
    return (model - data) / sigma


random.seed(0)
x = linspace(0.0, 20.0, 601)

data = (gaussian(x, 21, 8.1, 1.2) +
        lorentzian(x, 10, 9.6, 2.4) +
        random.normal(scale=0.23, size=x.size) +
        x*0.5)


pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)

sigma = 0.021  # estimate of data error (for all data points)

def __init__(self, independent_vars=['x'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super(LorentzianModel, self).__init__(lorentzian, **kwargs)
        self._set_paramhints_prefix()

def residual(pars, x, sigma=None, data=None):
    yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
    yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])

    slope = pars['line_slope']
    offset = pars['line_off']
    model = yg + yl + offset + x*slope

    if data is None:
        return model
    if sigma is None:
        return model - data
    return (model - data) / sigma