function  [f,v] = dlqrschurg(a,b,q,r)
%
%DLQRSCHURG  Discrete linear quadratic regulator solution
%  [f,v] = dlqschurg(a,b,q,r) solves the Riccati equation
%  associated with the real discrete time optimal linear regulator
%  problem of the form
%
%        min     sum {x'qx + u'ru}
%        st      x(t+1) = ax(t) + bu(t)
%
%  Returned are the matrices f and v such that the optimal decision rule
%  is -fx and the value function is x'vx
%
%  ALGORITHM: Generalized Schur  (without balancing)
%  REFERENCES: Anderson, Hansen, McGrattan and Sargent (1995) 
%             Pappas, Laub and Sandel (1980)
%  PROGRAM WRITTEN BY:  Evan W. Anderson   December 1, 1994


%Get the ordered generalized schur decomposition of (L,N) 

tol = 1e-15; 
n=size(a,1);
[U,LBAR,NBAR,alpha,beta,info] = schurg([eye(n) (b/r)*b'; zeros(n) a'], ...
                  [a zeros(n); -q eye(n)],0,0,tol);

%Calculate the solution to the Riccati equation and the optimal
% decision rule.  

v = U(n+1:2*n,1:n)/U(1:n,1:n);
f = (b'*v*b + r)\b'*v*a;