### Added logarithmic reduction algorithm to solve quadratic matrix equation.

`This algorithm is a slower alternative to the cyclic reduction algorithm (useful for testing purpose).`
parent 47e54340
 function [X1, info] = logarithmic_reduction(A,B,C,tol,maxit,check) %@info: %! @deftypefn {Function File} {[@var{X1}, @var{info}] =} logarithmic_reduction (@var{A},@var{B},@var{C},@var{tol},@var{maxit},@var{check}) %! @anchor{logarithmic_reduction} %! @sp 1 %! Solves the quadratic matrix equation AX^2 + BX + C = 0. %! @sp 2 %! @strong{Inputs} %! @sp 1 %! @table @ @var %! @item A %! Square matrix of doubles, n*n. %! @item B %! Square matrix of doubles, n*n. %! @item C %! Square matrix of doubles, n*n. %! @item tol %! Scalar double, tolerance parameter. %! @item maxit %! Scalar integer, maximum number of iterations. %! @item check %! Scalar integer, if non zero the solution is checked. %! @end table %! @sp 1 %! @strong{Outputs} %! @sp 1 %! @table @ @var %! @item X1 %! Square matrix of doubles, n*n, solution of the matrix equation. %! @item info %! Scalar integer, if nonzero the algorithm failed in finding the solution of the matrix equation. %! @end table %! @sp 2 %! @strong{This function is called by:} %! @sp 2 %! @strong{This function calls:} %! @sp 2 %! @strong{References:} %! @sp 1 %! G. Latouche and V. Ramaswami (1993), "A logarithmic reduction algorithm for Quasi-Birth-Death processes", in Journal of Applied Probability, Vol. 30, No. 3, pp. 650-674. %! @sp 2 %! @end deftypefn %@eod: % Copyright (C) 2012 Dynare Team % % This file is part of Dynare. % % Dynare is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % Dynare is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with Dynare. If not, see . info = 0; n = length(A); i = 1:n; tmp0 = -B\[A,C]; X0 = tmp0(:,n+i); U0 = tmp0(:,i); kk = 0; cc = 1; while cc>tol && kk<=maxit tmp1 = (eye(n)-tmp0*[tmp0(:,n+i);tmp0(:,i)])\[tmp0(:,i)*tmp0(:,i),tmp0(:,n+i)*tmp0(:,n+i)]; X1 = X0 + U0*tmp1(:,n+i); U1 = U0*tmp1(:,i); cc = max(max(abs(X1-X0))); X0 = X1; U0 = U1; tmp0 = tmp1; kk = kk+1; end if kk==maxit disp(['logarithmic_reduction:: Convergence not achieved after ' int2str(maxit) ' iterations!']); info = 1; end if nargin>5 && check if max(max(abs(A*X1*X1 + B*X1 + C)))>tol disp(['logarithmic_reduction:: Algotithm did not converge to the solution of the matrix quadratic equation!']); info = 1; end end \ No newline at end of file
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