function sp_lag_deriv_plot(y,X,W)

%plots the likelihood and derivative

n = length(y);

I = eye(n);

X = [ones(n,1),X];

M = I - X*inv(X'*X)*X';

val = real(eig(W));

r1 = 1/max(val);

r0 = 1/min(val);

lam = [r0/2  :(r1-r0)/100 : r1 - .0001];

N = length(lam);

L = zeros(N,1);

D = zeros(N,1);

LDET = zeros(N,1);

QUAD = zeros(N,1);

for i = 1:N
    
    B = I - lam(i)*W;    
   
    LDET(i) = log(det(B));
    
    QUAD(i) = -(n/2)*log(y'*B'*M*B*y);
    
    L(i) = LDET(i) + QUAD(i);    
    
    num = n*y'*M*W*y - lam(i)*n*y'*W'*M*W*y;

    denom = y'*B'*M*B*y;

    K1 = num/denom;

    vv = val./(1 - lam(i)*val);

    K2 = sum(vv);

    D(i) = K1 - K2;
    
end

plot(lam,L);

title('LOG LIKELIHOOD');

pause;

clf;

plot(lam,LDET,'r');

title('LOG DETERMINANT');

pause;

clf;

plot(lam,QUAD,'r');

title('QUADRATIC TERM');

pause;

clf;

plot(lam,D,'r');

title('DERIVATIVE');