function  [f,v] = dlqrdouble(a,b,q,r,tol,maxit)
%
%DLQRDOUBLE  Discrete linear quadratic regulator solution
%  [f,v] = dlqrdouble(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.   tol and maxit are optional
%  parameters.  If they both are not inputted then they are given 
%  default values.  See the m-file doubler.m for a description of
%  tol and maxit. 
%
%  ALGORITHM: Doubling algorithm
%  REFERENCES:  B.D.O Anderson (1978)
%  WRITTEN BY:  Evan W. Anderson   Dec  1, 1994
%  DOCUMENTATION MODIFIED:         Dec 29, 1998

if nargin < 6,
  tol = 1e-15;
  maxit = 1e4;
end
[v,info] = doubler(a,b*(r\b'),q,tol,maxit);
f = (b'*v*b + r)\b'*v*a;