/* loglike_mvgm.c 


  Compute the loglikelihood of mixture of Multivariate Gaussian pdf.


  Usage: logl = loglike_mvgm(Z , mu , sigma , p); 
  ------

  Inputs
  ------

	Z          Measure    (d x K x [s1] x ....x [sn])   
    mu         Mean parameters (d x 1 x [v1] x ... x [vp])
    sigma      Covariance parameters (d x d x [v1] x ... x [vp])
    p          Weight parameters  (1 x 1 x [v1] x ... x [vp]), sum(p) = 1

   Outputs
   -------

    logl       Loglikelihood ([s1] x ... x [sn] x [v1] x ... x [vp]) matrix.

  
    
		  
 Example 
 --------



 N       = 200;
 V       = 90;
 OV      = ones(1 , V);
  
 mu      = cat(3 , [-5 ; -5] , [0 ; 0] ,[ 5 ; 5]);                %(d x 1 x M)
 sigma   = cat(3 , [2 0; 0 1] , [2 -.2; -.2 2] , [1 .9; .9 1]  ); %(d x d x M)
 p       = cat(3 , [0.3] , [0.1]  , [0.6]);                       %(1 x 1 x M)
 M       = mu(: , : , : , OV) + 0.5*randn(2 , 1 , 3 , V);
 S       = sigma(: , : , : , OV) + 0.01*randn(2 , 2 , 3 , V);
 P       = p(: , : , : , OV);

 Z       = mvgmmrnd(N , mu , sigma , p);
 [x , y] = ndellipse(mu , sigma);
 [X , Y] = ndellipse(M , S);
 logl    = loglike_mvgm(Z , M , S , P);

 logltrue   = loglike_mvgm(Z , mu , sigma , p);
 figure(1)
 plot(Z(1 , :) , Z(2 , :) , 'k+',reshape(permute(X , [1 3 2]) , 50*V , 3) , reshape(permute(Y , [1 3 2]) , 50*V , 3)  , 'markersize' , 2 , 'linewidth' , 1);
 hold on
 plot( x , y , 'g'  , reshape(mu(1 , : , :) , 1 , 3) , reshape(mu(2 , : , :) , 1 , 3) , 'r+' , 'markersize' , 6 ,  'linewidth' , 2);
 hold off
 figure(2),plot(1:V , logl , 1:V , logltrue(: , ones(1 , V))),grid on


  
  To compile : 
  -----------

  mex -output loglike_mvgm.dll loglike_mvgm.c

  Myself, I use Intel CPP compiler as : 
  
  mex -f mexopts_intel10amd.bat -output loglike_mvgm.dll loglike_mvgm.c

  Ver 1.1 (03/26/05)

  Changle Log

  1.0 Initial release

  1.1 New Feature : nd slices measurements is now accepted



  Author : S閎astien PARIS