%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Name: M_step.m
% Input: x - a nxd matrix (nx3 if using RGB)
%        Q - vector of values from the complete data log-likelihood function
%        h - a nxk matrix, the expectation of the hidden variable z given the data set and distribution params
%        S - cluster covariance matrices
%        k - the number of clusters
%        flag - flag to use improved EM to avoid singular covariance matrix
% Output: S - cluster covariance matrices
%         m - cluster means
%         pi - mixing coefficients
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [S, m, pi] = M_step(x, h, S, k, flag)

  % get size of data
  [num_data, dim] = size(x);
  eps = 1e-15;
  lambda = 1e-3; % value for improved version of EM

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % TODO: update mixing coefficients
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
  

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % TODO: update cluster means
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % TODO: Calculate the covariance matrix estimate
  %       further modifications will need to be made when doing 2(d)
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


end