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Efficiency changes.

time-shift
Stéphane Adjemian (Charybdis) 2012-07-09 16:00:04 +02:00
parent 877cc55e78
commit b4c60eeebf
1 changed files with 38 additions and 39 deletions
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77
matlab/cycle_reduction.m
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@ -1,7 +1,7 @@
function [X, info] = cycle_reduction(A0, A1, A2, cvg_tol, ch)
% function [X, info] = cycle_reduction(A0,A1,A2,A3, cvg_tolch)
%
% Solves Polynomial Equation:
%
% Solves Polynomial Equation:
% A0 + A1 * X + A2 * X² = 0
% Using Cyclic Reduction algorithm
% - D.A. Bini, G. Latouche, B. Meini (2002), "Solving matrix polynomial equations arising in
@ -27,43 +27,42 @@ function [X, info] = cycle_reduction(A0, A1, A2, cvg_tol, ch)
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
max_it = 300;
it = 0;
info = 0;
crit = 1+cvg_tol;
A_0 = A1;
A0_0 = A0;
A1_0 = A1;
A2_0 = A2;
while crit > cvg_tol && it < max_it;
i_A1_0 = inv(A1_0);
A2_0_i_A1_0 = A2_0 * i_A1_0;
A0_0_i_A1_0 = A0_0 * i_A1_0;
A1_INC = A2_0_i_A1_0 * A0_0;
A_1 = A_0 - A1_INC;
A0_1 = - A0_0_i_A1_0 * A0_0;
A1_1 = A1_0 - A0_0_i_A1_0 * A2_0 - A1_INC;
A2_1 = - A2_0_i_A1_0 * A2_0;
max_it = 300;
it = 0;
info = 0;
crit = 1+cvg_tol;
A_0 = A1;
A0_0 = A0;
A1_0 = A1;
A2_0 = A2;
n = length(A0);
id = 1:n;
while crit > cvg_tol && it < max_it;
tmp = [A2_0; A0_0]/A1_0; % = [A2_0_i_A1_0; A0_0_i_A1_0]*inv(A1_0)
TMP = tmp*A0_0;
A2_1 = - tmp(id,:) * A2_0;
A_1 = A_0 - TMP(id,:);
A1_1 = A1_0 - tmp(n+id,:) * A2_0 - TMP(id,:);
crit = sum(sum(abs(A0_0)));
A_0 = A_1;
A0_0 = -TMP(n+id,:);
A1_0 = A1_1;
A2_0 = A2_1;
it = it + 1;
end
crit = sum(sum(abs(A0_0)));
if it==max_it
disp(['convergence not achieved after ' int2str(it) ' iterations']);
info = 1;
end
A_0 = A_1;
A0_0 = A0_1;
A1_0 = A1_1;
A2_0 = A2_1;
it = it + 1;
%disp(['it=' int2str(it) ' crit = ' num2str(crit)]);
end;
if it==max_it
disp(['convergence not achieved after ' int2str(it) ' iterations']);
info = 1;
end
X = - inv(A_0) * A0;
if (nargin == 5 && ~isempty( ch ) == 1 )
%check the solution
res = A0 + A1 * X + A2 * X * X;
if (sum(sum(abs(res))) > cvg_tol)
disp(['the norm residual of the residu ' num2str(res) ' compare to the tolerance criterion ' num2str(cvg_tol)]);
end;
end;
X = -A_0\A0;
if (nargin == 5 && ~isempty( ch ) == 1 )
%check the solution
res = A0 + A1 * X + A2 * X * X;
if (sum(sum(abs(res))) > cvg_tol)
disp(['the norm residual of the residu ' num2str(res) ' compare to the tolerance criterion ' num2str(cvg_tol)]);
end
end