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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _get_sigma_at_quantile(self, sigma_quantile):
 """ Calculates the total standard deviation at the specified quantile """

        # Mean mean is found in self.TAU. Get the variance in tau
        tau_std = TAU_SETUP[self.tau_model]["STD"]
        # Mean phiss is found in self.PHI_SS. Get the variance in phi
        phi_std = deepcopy(self.PHI_SS.sa_coeffs)
        phi_std.update(self.PHI_SS.non_sa_coeffs)
        for key in phi_std:
            phi_std[key] = {"a": PHI_SETUP[self.phi_model][key]["var_a"],
                            "b": PHI_SETUP[self.phi_model][key]["var_b"]}
        if self.ergodic:
            # IMT list should be taken from the PHI_S2SS_MODEL
            imt_list = list(
                PHI_S2SS_MODEL[self.phi_s2ss_model].non_sa_coeffs.keys())
            imt_list += \
                list(PHI_S2SS_MODEL[self.phi_s2ss_model].sa_coeffs.keys())
        else:
            imt_list = phi_std.keys()
        phi_std = CoeffsTable(sa_damping=5, table=phi_std)
        tau_bar, tau_std = self._get_tau_vector(self.TAU, tau_std, imt_list)
        phi_bar, phi_std = self._get_phi_vector(self.PHI_SS, phi_std, imt_list)
        sigma = {}
        # Calculate the total standard deviation
        for imt in imt_list:
            sigma[imt] = {}
            for i, key in enumerate(self.tau_keys):
                # Calculates the expected standard deviation
                sigma_bar = np.sqrt(tau_bar[imt][i] ** 2. +
                                    phi_bar[imt][i] ** 2.)
                # Calculated the variance in the standard deviation
                sigma_std = np.sqrt(tau_std[imt][i] ** 2. +
                                    phi_std[imt][i] ** 2.)
                # The keys swap from tau to sigma
                new_key = key.replace("tau", "sigma")
                if sigma_quantile is not None:
                    sigma[imt][new_key] =\
                        _at_percentile(sigma_bar, sigma_std, sigma_quantile)
                else:
                    sigma[imt][new_key] = sigma_bar
                self.tau_keys[i] = new_key
        self.SIGMA = CoeffsTable(sa_damping=5, table=sigma)