function [mu, B] = clg_Mstep(w, Y, YY, YTY, X, XX, XY)% CLG_MSTEP_SIMPLE Same as CLG_MSTEP, but doesn;t estimate Sigma, and has no optional args, so is slightly faster% function [mu, B] = clg_Mstep(w, Y, YY, YTY, X, XX, XY)%% We fit P(Y|X,Q=i) = N(Y; B_i X + mu_i, Sigma_i) % and w(i,t) = p(M(t)=i|y(t)) = posterior responsibility% See www.ai.mit.edu/~murphyk/Papers/learncg.pdf.%%% INPUTS:% w(i) = sum_t w(i,t) = responsibilities for each mixture component%  If there is only one mixture component (i.e., Q does not exist),%  then w(i) = N = nsamples,  and %  all references to i can be replaced by 1.% Y(:,i) = sum_t w(i,t) y(:,t) = weighted observations% YY(:,:,i) = sum_t w(i,t) y(:,t) y(:,t)' = weighted outer product% YTY(i) = sum_t w(i,t) y(:,t)' y(:,t) = weighted inner product%   You only need to pass in YTY if Sigma is to be estimated as spherical.%% In the regression context, we must also pass in the following% X(:,i) = sum_t w(i,t) x(:,t) = weighted inputs% XX(:,:,i) = sum_t w(i,t) x(:,t) x(:,t)' = weighted outer product% XY(i) = sum_t w(i,t) x(:,t) y(:,t)' = weighted outer product[Ysz Q] = size(Y);if isempty(X) % no regression  %B = [];  B2 = zeros(Ysz, 1, Q);  for i=1:Q    B(:,:,i) = B2(:,1:0,i); % make an empty array of size Ysz x 0 x Q  end  [mu, Sigma] = mixgauss_Mstep(w, Y, YY, YTY, varargin{:});  return;endN = sum(w);%YY = YY + cov_prior; % regularize the scatter matrix% Set any zero weights to one before dividing% This is valid because w(i)=0 => Y(:,i)=0, etcw = w + (w==0);Xsz = size(X,1);% Append 1 to X to get ZZZ = zeros(Xsz+1, Xsz+1, Q);ZY = zeros(Xsz+1, Ysz, Q);for i=1:Q  ZZ(:,:,i) = [XX(:,:,i)  X(:,i);	       X(:,i)'    w(i)];  ZY(:,:,i) = [XY(:,:,i);	       Y(:,i)'];end%%% Estimate mean and regression mu = zeros(Ysz, Q);B = zeros(Ysz, Xsz, Q);% Nothing is clamped, so we must estimate B and mu jointlyfor i=1:Q  % eqn 9  if rcond(ZZ(:,:,i)) < 1e-10    sprintf('clg_Mstep warning: ZZ(:,:,%d) is ill-conditioned', i);    %probably because there are too few cases for a high-dimensional input    ZZ(:,:,i) = ZZ(:,:,i) + 1e-5*eye(Xsz+1);  end  %A = ZY(:,:,i)' * inv(ZZ(:,:,i));  A = (ZZ(:,:,i) \ ZY(:,:,i))';  B(:,:,i) = A(:, 1:Xsz);  mu(:,i) = A(:, Xsz+1);end