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function P=lyapunov_solver(T,R,Q,DynareOptions) % --*-- Unitary tests --*--
% function P=lyapunov_solver(T,R,Q,DynareOptions)
% Solves the Lyapunov equation P-T*P*T' = R*Q*R' arising in a state-space
% system, where P is the variance of the states
%
% Inputs
% T [double] n*n matrix.
% R [double] n*m matrix.
% Q [double] m*m matrix.
% DynareOptions [structure] Dynare options
%
% Outputs
% P [double] n*n matrix.
%
% Algorithms
% Default, if none of the other algorithms is selected:
% Reordered Schur decomposition (Bartels-Stewart algorithm)
% DynareOptions.lyapunov_fp == 1
% iteration-based fixed point algorithm
% DynareOptions.lyapunov_db == 1
% doubling algorithm
% DynareOptions.lyapunov_srs == 1
% Square-root solver for discrete-time Lyapunov equations (requires Matlab System Control toolbox
% or Octave control package)
% Copyright (C) 2016-2017 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 <http://www.gnu.org/licenses/>.
if DynareOptions.lyapunov_fp == 1
P = lyapunov_symm(T,R*Q'*R',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, 3, DynareOptions.debug);
elseif DynareOptions.lyapunov_db == 1
[P, errorflag] = disclyap_fast(T,R*Q*R',DynareOptions.lyapunov_doubling_tol);
if errorflag %use Schur-based method
P = lyapunov_symm(T,R*Q*R',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], DynareOptions.debug);
end
elseif DynareOptions.lyapunov_srs == 1
% works only with Matlab System Control toolbox or Octave control package,
if isoctave
if ~user_has_octave_forge_package('control')
error('lyapunov=square_root_solver not available; you must install the control package from Octave Forge')
end
else
if ~user_has_matlab_license('control_toolbox')
error('lyapunov=square_root_solver not available; you must install the control system toolbox')
end
end
chol_Q = R*chol(Q,'lower');
R_P = dlyapchol(T,chol_Q);
P = R_P' * R_P;
else
P = lyapunov_symm(T,R*Q*R',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], DynareOptions.debug);
end
%@test:1
%$ t = NaN(10,1);
%$ options_.lyapunov_complex_threshold = 1e-15;
%$ options_.qz_zero_threshold = 1e-6;
%$ options_.qz_criterium=1-options_.qz_zero_threshold;
%$ options_.lyapunov_fixed_point_tol = 1e-10;
%$ options_.lyapunov_doubling_tol = 1e-16;
%$ options_.debug=0;
%$
%$ n_small=8;
%$ m_small=10;
%$ T_small=randn(n_small,n_small);
%$ T_small=0.99*T_small/max(abs(eigs(T_small)));
%$ tmp2=randn(m_small,m_small);
%$ Q_small=tmp2*tmp2';
%$ R_small=randn(n_small,m_small);
%$
%$ n_large=9;
%$ m_large=11;
%$ T_large=randn(n_large,n_large);
%$ T_large=0.99*T_large/max(abs(eigs(T_large)));
%$ tmp2=randn(m_large,m_large);
%$ Q_large=tmp2*tmp2';
%$ R_large=randn(n_large,m_large);
%$
%$ % DynareOptions.lyapunov_fp == 1
%$ options_.lyapunov_fp = 1;
%$ try
%$ Pstar1_small = lyapunov_solver(T_small,R_small,Q_small,options_);
%$ Pstar1_large = lyapunov_solver(T_large,R_large,Q_large,options_);
%$ t(1) = 1;
%$ catch
%$ t(1) = 0;
%$ end
%$
%$ % Dynareoptions.lyapunov_db == 1
%$ options_.lyapunov_fp = 0;
%$ options_.lyapunov_db = 1;
%$ try
%$ Pstar2_small = lyapunov_solver(T_small,R_small,Q_small,options_);
%$ Pstar2_large = lyapunov_solver(T_large,R_large,Q_large,options_);
%$ t(2) = 1;
%$ catch
%$ t(2) = 0;
%$ end
%$
%$ % Dynareoptions.lyapunov_srs == 1
%$ if (isoctave && user_has_octave_forge_package('control')) || (~isoctave && user_has_matlab_license('control_toolbox'))
%$ options_.lyapunov_db = 0;
%$ options_.lyapunov_srs = 1;
%$ try
%$ Pstar3_small = lyapunov_solver(T_small,R_small,Q_small,options_);
%$ Pstar3_large = lyapunov_solver(T_large,R_large,Q_large,options_);
%$ t(3) = 1;
%$ catch
%$ t(3) = 0;
%$ end
%$ else
%$ t(3) = 1;
%$ end
%$
%$ % Standard
%$ options_.lyapunov_srs = 0;
%$ try
%$ Pstar4_small = lyapunov_solver(T_small,R_small,Q_small,options_);
%$ Pstar4_large = lyapunov_solver(T_large,R_large,Q_large,options_);
%$ t(4) = 1;
%$ catch
%$ t(4) = 0;
%$ end
%$
%$ % Test the results.
%$
%$ if max(max(abs(Pstar1_small-Pstar2_small)))>1e-8
%$ t(5) = 0;
%$ else
%$ t(5) = 1;
%$ end
%$
%$ if (isoctave && user_has_octave_forge_package('control')) || (~isoctave && user_has_matlab_license('control_toolbox'))
%$ if max(max(abs(Pstar1_small-Pstar3_small)))>1e-8
%$ t(6) = 0;
%$ else
%$ t(6) = 1;
%$ end
%$ else
%$ t(6) = 1;
%$ end
%$
%$ if max(max(abs(Pstar1_small-Pstar4_small)))>1e-8
%$ t(7) = 0;
%$ else
%$ t(7) = 1;
%$ end
%$
%$ if max(max(abs(Pstar1_large-Pstar2_large)))>1e-8
%$ t(8) = 0;
%$ else
%$ t(8) = 1;
%$ end
%$
%$ if (isoctave && user_has_octave_forge_package('control')) || (~isoctave && user_has_matlab_license('control_toolbox'))
%$ if max(max(abs(Pstar1_large-Pstar3_large)))>1e-8
%$ t(9) = 0;
%$ else
%$ t(9) = 1;
%$ end
%$ else
%$ t(9) = 1;
%$ end
%$
%$ if max(max(abs(Pstar1_large-Pstar4_large)))>1e-8
%$ t(10) = 0;
%$ else
%$ t(10) = 1;
%$ end
%$
%$ T = all(t);
%@eof:1
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