function  [f,v] = dlqrriccati(a,b,q,r,tol,maxit)
%
%DLQRRICCATI  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 riccati.m for a description of
%  tol and maxit. 

%
%  ALGORITHM: Riccati Equation Iteration
%  REFERENCES: E.W. Anderson, L.P. Hansen, E.R McGrattan and T.J Sargent(1996)
%  WRITTEN BY:  Evan W. Anderson   December 1, 1994

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