function a = gmmactiv(mix, x)%GMMACTIV Computes the activations of a Gaussian mixture model.%%	Description%	This function computes the activations A (i.e. the  probability%	P(X|J) of the data conditioned on each component density)  for a%	Gaussian mixture model.  For the PPCA model, each activation is the%	conditional probability of X given that it is generated by the%	component subspace. The data structure MIX defines the mixture model,%	while the matrix X contains the data vectors.  Each row of X%	represents a single vector.%%	See also%	GMM, GMMPOST, GMMPROB%%	Copyright (c) Ian T Nabney (1996-2001)% Check that inputs are consistenterrstring = consist(mix, 'gmm', x);if ~isempty(errstring)  error(errstring);endndata = size(x, 1);a = zeros(ndata, mix.ncentres);  % Preallocate matrixswitch mix.covar_type  case 'spherical'  % Calculate squared norm matrix, of dimension (ndata, ncentres)  n2 = dist2(x, mix.centres);    % Calculate width factors  wi2 = ones(ndata, 1) * (2 .* mix.covars);  normal = (pi .* wi2) .^ (mix.nin/2);    % Now compute the activations  a = exp(-(n2./wi2))./ normal;  case 'diag'  normal = (2*pi)^(mix.nin/2);  s = prod(sqrt(mix.covars), 2);  for j = 1:mix.ncentres    diffs = x - (ones(ndata, 1) * mix.centres(j, :));    a(:, j) = exp(-0.5*sum((diffs.*diffs)./(ones(ndata, 1) * ...      mix.covars(j, :)), 2)) ./ (normal*s(j));  end  case 'full'  normal = (2*pi)^(mix.nin/2);  for j = 1:mix.ncentres    diffs = x - (ones(ndata, 1) * mix.centres(j, :));    % Use Cholesky decomposition of covariance matrix to speed computation    c = chol(mix.covars(:, :, j));    temp = diffs/c;    a(:, j) = exp(-0.5*sum(temp.*temp, 2))./(normal*prod(diag(c)));  endcase 'ppca'  log_normal = mix.nin*log(2*pi);  d2 = zeros(ndata, mix.ncentres);  logZ = zeros(1, mix.ncentres);  for i = 1:mix.ncentres    k = 1 - mix.covars(i)./mix.lambda(i, :);    logZ(i) = log_normal + mix.nin*log(mix.covars(i)) - ...      sum(log(1 - k));    diffs = x - ones(ndata, 1)*mix.centres(i, :);    proj = diffs*mix.U(:, :, i);    d2(:,i) = (sum(diffs.*diffs, 2) - ...      sum((proj.*(ones(ndata, 1)*k)).*proj, 2)) / ...      mix.covars(i);  end  a = exp(-0.5*(d2 + ones(ndata, 1)*logZ));otherwise  error(['Unknown covariance type ', mix.covar_type]);end