ProductInt

   Product and marginalization of two GMixtures.

   Returns the result of multiplying two Gaussian mixtures and then
   marginalizing all over the space where those Gaussians are defined.
   The result is the sum of the product of pairs of weights in the
   mixtures and the normalization factor of multiplying the corresponding
   Gaussians.
   This is used in Section 5.2 of the paper to compute tha alpha functions
   to be used in the Backup.
 
   See also @Gaussian/ProductNormFator.

0001 function c=ProductInt(gm1,gm2)
0002 %   Product and marginalization of two GMixtures.
0003 %
0004 %   Returns the result of multiplying two Gaussian mixtures and then
0005 %   marginalizing all over the space where those Gaussians are defined.
0006 %   The result is the sum of the product of pairs of weights in the
0007 %   mixtures and the normalization factor of multiplying the corresponding
0008 %   Gaussians.
0009 %   This is used in Section 5.2 of the paper to compute tha alpha functions
0010 %   to be used in the Backup.
0011 %
0012 %   See also @Gaussian/ProductNormFator.
0013 
0014   c=0.0;
0015   if gm1.n>0
0016     %z=0*get(gm1.g{1},'mean');
0017     for i=1:gm1.n
0018       m1=get(gm1.g{i},'mean');
0019       S1=get(gm1.g{i},'covariance');
0020       val=cellfun(@(x)(Value(Gaussian(get(x,'mean'),S1+get(x,'covariance')),m1)),gm2.g);
0021       c=c+gm1.w(i)*sum(gm2.w.*val);
0022     end
0023   end