You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: mixing.m
    path of file: ./repos/M-SPARC/src
    
    the code of the file until where you have to start completion: function [S,x_kp1] = mixing(S, g_k, x_k, iter)
% @brief    MIXING performs mixing of the previous SCF iterates to 
%           accelerate SCF convergence.
%
% @param g_k    Current output mixing iterate.
% @param x_in   Current input mixing iterate.
% @param iter   Iteration number.
%
% @authors  Qimen Xu <qimenxu@gatech.edu>
%           Abhiraj Sharma <asharma424@gatech.edu>
%           Phanish Suryanarayana <phanish.suryanarayana@ce.gatech.edu>
%
% @copyright (c) 2019 Material Physics & Mechanics Group, Georgia 
    
function [S,x_kp1] = Periodic_Pulay(S, g_k, x_k, iter)
% periodic pulay mixing
% Ref: A Banerjee et al, Chemical Physics Letters 647 (2016) 31-35.
%      http://dx.doi.org/10.1016/j.cplett.2016.01.033
m = S.MixingHistory; 
p = S.PulayFrequency;
beta = S.MixingParameter; % beta
omega = S.MixingParameterSimple; % mixing parameter for simple mixing step
beta_mag = S.MixingParameterMag;
omega_mag = S.MixingParameterSimpleMag;

Pulay_mixing_flag = (rem(iter,p) == 0 && iter > 1);

if Pulay_mixing_flag   % paulay mixing
    amix = beta; amix_mag = beta_mag;
else                   % simple (linear) mixing
    amix = omega; amix_mag = omega_mag;
end