function L = sar_lik(rho,low,high,val,W,e,X)

%SAR_LIK is the (negative) concentrated B = sparse(eye(n) - rho*W) ;
%likelihood function
%
%INPUTS: (i)   z = vector of parameters
%              z(1) = rho
%        (ii)   W = weight matrix
%        (iii)  e = residual n-vector
%        (iv)   X = (nxkk)data matrix (kk = k+1 includes 1-vector) 
%        
%OUTPUT: L = value of likelihood 

[n,kk] =  size(X) ;


rho = min([rho,high - .001]) ;

rho = max([rho,low + .001]) ;


B = speye(n) - rho*sparse(W) ;

LogDet = sum(log(1 - rho*val)) ;

L = (n/2)*log(e'*B'*B*e) - LogDet;