function L = lam_lik(lam,y,e,W)

%LAM_LIK is the (negative) concentrated likelihood function for lamda
%
%INPUTS: (i)    lam = value of lam
%        (ii)   W = weight matrix
%        (iii)  e = error vector
%        
%OUTPUT: L = value of concentrated likelihood 

n = length(W) ;

B = sparse( eye(n) - lam * W) ;

d = det(B) ;

if d <= 0
   
   error('matrix (I-lam*W) is not pd')
   
end

L = (n/2)*log((1/n)*(e - lam*W*y)'*(e - lam*W*y)) - log(det(B));