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Merge pull request #983 from JohannesPfeifer/lyap_fix 

Two fixes regarding solution of lyapunov equations
time-shift
MichelJuillard 2015-07-23 15:55:12 +02:00
parent 53fef04e29 0fd76e0c6f
commit 13cb9930f4
12 changed files with 62 additions and 49 deletions
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12
matlab/DsgeSmoother.m
View File

@ -128,13 +128,13 @@ if options_.lik_init == 1 % Kalman filter
kalman_algo = 1;
end
if options_.lyapunov_fp == 1
Pstar = lyapunov_symm(T,R*Q*R',options_.lyapunov_fixed_point_tol,options_.lyapunov_complex_threshold, 3, [], options_.debug);
Pstar = lyapunov_symm(T,R*Q*R',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, [], options_.debug);
elseif options_.lyapunov_db == 1
Pstar = disclyap_fast(T,R*Q*R',options_.lyapunov_doubling_tol);
elseif options_.lyapunov_srs == 1
Pstar = lyapunov_symm(T,Q,options_.lyapunov_fixed_point_tol,options_.lyapunov_complex_threshold, 4, R, options_.debug);
Pstar = lyapunov_symm(T,Q,options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 4, R, options_.debug);
else
Pstar = lyapunov_symm(T,R*Q*R',options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
Pstar = lyapunov_symm(T,R*Q*R',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
end;
Pinf = [];
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
@ -171,13 +171,13 @@ elseif options_.lik_init == 5 % Old diffuse Kalman filter only for th
R_tmp = R(stable, :);
T_tmp = T(stable,stable);
if options_.lyapunov_fp == 1
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',options_.lyapunov_fixed_point_tol,options_.lyapunov_complex_threshold, 3, [], options_.debug);
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 3, [], options_.debug);
elseif options_.lyapunov_db == 1
Pstar_tmp = disclyap_fast(T_tmp,R_tmp*Q*R_tmp',options_.lyapunov_doubling_tol);
elseif options_.lyapunov_srs == 1
Pstar_tmp = lyapunov_symm(T_tmp,Q,options_.lyapunov_fixed_point_tol,options_.lyapunov_complex_threshold, 4, R_tmp, options_.debug);
Pstar_tmp = lyapunov_symm(T_tmp,Q,options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, 4, R_tmp, options_.debug);
else
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
end
Pstar(stable, stable) = Pstar_tmp;
Pinf = [];

2
matlab/UnivariateSpectralDensity.m
View File

@ -93,7 +93,7 @@ for i=M_.maximum_lag:-1:2
end
Gamma = zeros(nvar,cutoff+1);
[A,B] = kalman_transition_matrix(dr,ikx',1:nx,M_.exo_nbr);
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
iky = iv(ivar);
if ~isempty(u)
iky = iky(find(any(abs(ghx(iky,:)*u) < options_.Schur_vec_tol,2)));

22
matlab/dsge_likelihood.m
View File

@ -370,13 +370,13 @@ switch DynareOptions.lik_init
kalman_algo = 1;
end
if DynareOptions.lyapunov_fp == 1
Pstar = lyapunov_symm(T,R*Q'*R',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.lyapunov_complex_threshold, 3, [], DynareOptions.debug);
Pstar = 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
Pstar = disclyap_fast(T,R*Q*R',DynareOptions.lyapunov_doubling_tol);
elseif DynareOptions.lyapunov_srs == 1
Pstar = lyapunov_symm(T,Q,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.lyapunov_complex_threshold, 4, R, DynareOptions.debug);
Pstar = lyapunov_symm(T,Q,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, 4, R, DynareOptions.debug);
else
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
end;
Pinf = [];
a = zeros(mm,1);
@ -472,7 +472,7 @@ switch DynareOptions.lik_init
if err
disp(['dsge_likelihood:: I am not able to solve the Riccati equation, so I switch to lik_init=1!']);
DynareOptions.lik_init = 1;
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
end
Pinf = [];
a = zeros(mm,1);
@ -493,13 +493,13 @@ switch DynareOptions.lik_init
R_tmp = R(stable, :);
T_tmp = T(stable,stable);
if DynareOptions.lyapunov_fp == 1
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.lyapunov_complex_threshold, 3, [], DynareOptions.debug);
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, 3, [], DynareOptions.debug);
elseif DynareOptions.lyapunov_db == 1
Pstar_tmp = disclyap_fast(T_tmp,R_tmp*Q*R_tmp',DynareOptions.lyapunov_doubling_tol);
elseif DynareOptions.lyapunov_srs == 1
Pstar_tmp = lyapunov_symm(T_tmp,Q,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.lyapunov_complex_threshold, 4, R_tmp, DynareOptions.debug);
Pstar_tmp = lyapunov_symm(T_tmp,Q,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, 4, R_tmp, DynareOptions.debug);
else
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
Pstar_tmp = lyapunov_symm(T_tmp,R_tmp*Q*R_tmp',DynareOptions.qz_criterium,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
end
Pstar(stable, stable) = Pstar_tmp;
Pinf = [];
@ -579,14 +579,14 @@ if analytic_derivation,
for i=1:EstimatedParameters.nvx
k =EstimatedParameters.var_exo(i,1);
DQ(k,k,i) = 2*sqrt(Q(k,k));
dum = lyapunov_symm(T,DOm(:,:,i),DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
dum = lyapunov_symm(T,DOm(:,:,i),DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
% kk = find(abs(dum) < 1e-12);
% dum(kk) = 0;
DP(:,:,i)=dum;
if full_Hess
for j=1:i,
jcount=jcount+1;
dum = lyapunov_symm(T,dyn_unvech(D2Om(:,jcount)),DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
dum = lyapunov_symm(T,dyn_unvech(D2Om(:,jcount)),DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
% kk = (abs(dum) < 1e-12);
% dum(kk) = 0;
D2P(:,jcount)=dyn_vech(dum);
@ -606,7 +606,7 @@ if analytic_derivation,
offset = offset + EstimatedParameters.nvn;
if DynareOptions.lik_init==1,
for j=1:EstimatedParameters.np
dum = lyapunov_symm(T,DT(:,:,j+offset)*Pstar*T'+T*Pstar*DT(:,:,j+offset)'+DOm(:,:,j+offset),DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
dum = lyapunov_symm(T,DT(:,:,j+offset)*Pstar*T'+T*Pstar*DT(:,:,j+offset)'+DOm(:,:,j+offset),DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
% kk = find(abs(dum) < 1e-12);
% dum(kk) = 0;
DP(:,:,j+offset)=dum;
@ -620,7 +620,7 @@ if analytic_derivation,
D2Tij = reshape(D2T(:,jcount),size(T));
D2Omij = dyn_unvech(D2Om(:,jcount));
tmp = D2Tij*Pstar*T' + T*Pstar*D2Tij' + DTi*DPj*T' + DTj*DPi*T' + T*DPj*DTi' + T*DPi*DTj' + DTi*Pstar*DTj' + DTj*Pstar*DTi' + D2Omij;
dum = lyapunov_symm(T,tmp,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
dum = lyapunov_symm(T,tmp,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
% dum(abs(dum)<1.e-12) = 0;
D2P(:,jcount) = dyn_vech(dum);
% D2P(:,:,j+offset,i) = dum;

2
matlab/dsge_var_likelihood.m
View File

@ -162,7 +162,7 @@ end
%------------------------------------------------------------------------------
% Compute the theoretical second order moments
tmp0 = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
tmp0 = lyapunov_symm(T,R*Q*R',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold, [], [], DynareOptions.debug);
mf = BayesInfo.mf1;
% Get the non centered second order moments

6
matlab/getJJ.m
View File

@ -64,7 +64,7 @@ else
% return
% end
m = length(A);
GAM = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium,options_.lyapunov_complex_threshold,1,[],options_.debug);
GAM = lyapunov_symm(A,B*M_.Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,1,[],options_.debug);
k = find(abs(GAM) < 1e-12);
GAM(k) = 0;
% if useautocorr,
@ -78,7 +78,7 @@ else
% end
% XX = lyapunov_symm_mr(A,BB,options_.qz_criterium,options_.lyapunov_complex_threshold,0);
for j=1:length(indexo),
dum = lyapunov_symm(A,dOm(:,:,j),options_.qz_criterium,options_.lyapunov_complex_threshold,2,[],options_.debug);
dum = lyapunov_symm(A,dOm(:,:,j),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,2,[],options_.debug);
% dum = XX(:,:,j);
k = find(abs(dum) < 1e-12);
dum(k) = 0;
@ -103,7 +103,7 @@ else
end
nexo = length(indexo);
for j=1:length(indx),
dum = lyapunov_symm(A,dA(:,:,j+nexo)*GAM*A'+A*GAM*dA(:,:,j+nexo)'+dOm(:,:,j+nexo),options_.qz_criterium,options_.lyapunov_complex_threshold,2,[],options_.debug);
dum = lyapunov_symm(A,dA(:,:,j+nexo)*GAM*A'+A*GAM*dA(:,:,j+nexo)'+dOm(:,:,j+nexo),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,2,[],options_.debug);
% dum = XX(:,:,j);
k = find(abs(dum) < 1e-12);
dum(k) = 0;

2
matlab/get_variance_of_endogenous_variables.m
View File

@ -45,7 +45,7 @@ n = length(i_var);
[A,B] = kalman_transition_matrix(dr,nstatic+(1:nspred),1:nc,M_.exo_nbr);
[vx,u] = lyapunov_symm(A,B*Sigma_e*B',options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
[vx,u] = lyapunov_symm(A,B*Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold, [], [], options_.debug);
if size(u,2) > 0
i_stat = find(any(abs(ghx*u) < options_.Schur_vec_tol,2)); %only set those variances of objective function for which variance is finite

28
matlab/lyapunov_symm.m
View File

@ -1,14 +1,12 @@
function [x,u] = lyapunov_symm(a,b,third_argument,lyapunov_complex_threshold,method, R, debug) % --*-- Unitary tests --*--
function [x,u] = lyapunov_symm(a,b,lyapunov_fixed_point_tol,qz_criterium,lyapunov_complex_threshold,method, R, debug) % --*-- Unitary tests --*--
% Solves the Lyapunov equation x-a*x*a' = b, for b and x symmetric matrices.
% If a has some unit roots, the function computes only the solution of the stable subsystem.
%
% INPUTS:
% a [double] n*n matrix.
% b [double] n*n matrix.
% third_argument [double] scalar, if method <= 2 :
% qz_criterium = third_argument unit root threshold for eigenvalues in a,
% elseif method = 3 :
% tol =third_argument the convergence criteria for fixed_point algorithm.
% qz_criterium [double] unit root threshold for eigenvalues
% lyapunov_fixed_point_tol [double] convergence criteria for fixed_point algorithm.
% lyapunov_complex_threshold [double] scalar, complex block threshold for the upper triangular matrix T.
% method [integer] Scalar, if method=0 [default] then U, T, n and k are not persistent.
% method=1 then U, T, n and k are declared as persistent
@ -44,11 +42,11 @@ function [x,u] = lyapunov_symm(a,b,third_argument,lyapunov_complex_threshold,met
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
if nargin<5 || isempty(method)
if nargin<6 || isempty(method)
method = 0;
end
if nargin<7
if nargin<8
debug = 0;
end
@ -57,7 +55,6 @@ if method == 3
if ~isempty(method1)
method = method1;
end;
tol = third_argument;
if debug
fprintf('lyapunov_symm:: [method=%d] \n',method);
end
@ -73,7 +70,7 @@ if method == 3
end;
at = a';
%fixed point iterations
while evol > tol && it_fp < max_it_fp;
while evol > lyapunov_fixed_point_tol && it_fp < max_it_fp;
X_old = X;
X = a * X * at + b;
evol = max(sum(abs(X - X_old))); %norm_1
@ -110,7 +107,6 @@ elseif method == 4
return;
end;
qz_criterium = third_argument;
if method
persistent U T k n
else
@ -210,8 +206,8 @@ u = U(:,1:k);
%$
%$ % DynareOptions.lyapunov_fp == 1
%$ try
%$ Pstar1_small = lyapunov_symm(T_small,R_small*Q_small*R_small',lyapunov_fixed_point_tol,lyapunov_fixed_point_tol,3, [], 0);
%$ Pstar1_large = lyapunov_symm(T_large,R_large*Q_large*R_large',lyapunov_fixed_point_tol,lyapunov_fixed_point_tol,3, [], 0);
%$ Pstar1_small = lyapunov_symm(T_small,R_small*Q_small*R_small',lyapunov_fixed_point_tol,qz_criterium,lyapunov_complex_threshold,3, [], 0);
%$ Pstar1_large = lyapunov_symm(T_large,R_large*Q_large*R_large',lyapunov_fixed_point_tol,qz_criterium,lyapunov_complex_threshold,3, [], 0);
%$ t(1) = 1;
%$ catch
%$ t(1) = 0;
@ -229,8 +225,8 @@ u = U(:,1:k);
%$ % Dynareoptions.lyapunov_srs == 1
%$ if (isoctave && user_has_octave_forge_package('control')) || (~isoctave && user_has_matlab_license('control_toolbox'))
%$ try
%$ Pstar3_small = lyapunov_symm(T_small,Q_small,lyapunov_fixed_point_tol,lyapunov_complex_threshold,4,R_small,0);
%$ Pstar3_large = lyapunov_symm(T_large,Q_large,lyapunov_fixed_point_tol,lyapunov_complex_threshold,4,R_large,0);
%$ Pstar3_small = lyapunov_symm(T_small,Q_small,lyapunov_fixed_point_tol,qz_criterium,lyapunov_complex_threshold,4,R_small,0);
%$ Pstar3_large = lyapunov_symm(T_large,Q_large,lyapunov_fixed_point_tol,qz_criterium,lyapunov_complex_threshold,4,R_large,0);
%$ t(3) = 1;
%$ catch
%$ t(3) = 0;
@ -241,8 +237,8 @@ u = U(:,1:k);
%$
%$ % Standard
%$ try
%$ Pstar4_small = lyapunov_symm(T_small,R_small*Q_small*R_small',qz_criterium, lyapunov_complex_threshold, [], [], 0);
%$ Pstar4_large = lyapunov_symm(T_large,R_large*Q_large*R_large',qz_criterium, lyapunov_complex_threshold, [], [], 0);
%$ Pstar4_small = lyapunov_symm(T_small,R_small*Q_small*R_small',lyapunov_fixed_point_tol,qz_criterium, lyapunov_complex_threshold, [], [], 0);
%$ Pstar4_large = lyapunov_symm(T_large,R_large*Q_large*R_large',lyapunov_fixed_point_tol,qz_criterium, lyapunov_complex_threshold, [], [], 0);
%$ t(4) = 1;
%$ catch
%$ t(4) = 0;

2
matlab/non_linear_dsge_likelihood.m
View File

@ -271,7 +271,7 @@ ReducedForm.mf1 = mf1;
switch DynareOptions.particle.initialization
case 1% Initial state vector covariance is the ergodic variance associated to the first order Taylor-approximation of the model.
StateVectorMean = ReducedForm.constant(mf0);
StateVectorVariance = lyapunov_symm(ReducedForm.ghx(mf0,:),ReducedForm.ghu(mf0,:)*ReducedForm.Q*ReducedForm.ghu(mf0,:)',1e-12,1e-12,[],[],DynareOptions.debug);
StateVectorVariance = lyapunov_symm(ReducedForm.ghx(mf0,:),ReducedForm.ghu(mf0,:)*ReducedForm.Q*ReducedForm.ghu(mf0,:)',DynareOptions.lyapunov_fixed_point_tol,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold,[],[],DynareOptions.debug);
case 2% Initial state vector covariance is a monte-carlo based estimate of the ergodic variance (consistent with a k-order Taylor-approximation of the model).
StateVectorMean = ReducedForm.constant(mf0);
old_DynareOptionsperiods = DynareOptions.periods;

25
matlab/partial_information/disclyap_fast.m
View File

@ -1,6 +1,14 @@
function X=disclyap_fast(G,V,tol,ch)
function [X,exitflag]=disclyap_fast(G,V,tol,ch)
% function X=disclyap_fast(G,V,ch)
%
% Inputs:
% - G [double] first input matrix
% - V [double] second input matrix
% - tol [scalar] tolerance criterion
% - ch empty of non-empty if non-empty: check positive-definiteness
% Outputs:
% - X [double] solution matrix
% - exitflag [scalar] 0 if solution is found, 1 otherwise
%
% Solve the discrete Lyapunov Equation
% X=G*X*G'+V
% Using the Doubling Algorithm
@ -11,7 +19,7 @@ function X=disclyap_fast(G,V,tol,ch)
% Joe Pearlman and Alejandro Justiniano
% 3/5/2005
% Copyright (C) 2010-2012 Dynare Team
% Copyright (C) 2010-2015 Dynare Team
%
% This file is part of Dynare.
%
@ -34,6 +42,7 @@ else
flag_ch = 1;
end
s=size(G,1);
exitflag=0;
%tol = 1e-16;
@ -41,13 +50,20 @@ P0=V;
A0=G;
matd=1;
while matd > tol
iter=1;
while matd > tol && iter< 2000
P1=P0+A0*P0*A0';
A1=A0*A0;
matd=max( max( abs( P1 - P0 ) ) );
P0=P1;
A0=A1;
iter=iter+1;
end
if iter==5000
X=NaN(P0);
exitflag=1;
return
end
clear A0 A1 P1;
X=(P0+P0')/2;
@ -56,6 +72,7 @@ X=(P0+P0')/2;
if flag_ch==1
[C,p]=chol(X);
if p ~= 0
exitflag=1;
error('X is not positive definite')
end
end

6
matlab/th_autocovariances.m
View File

@ -129,7 +129,7 @@ end;
% and compute 2nd order mean correction on stationary variables (in case of
% HP filtering, this mean correction is computed *before* filtering)
if options_.order == 2 || options_.hp_filter == 0
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
if options_.block == 0
iky = inv_order_var(ivar);
else
@ -188,11 +188,11 @@ if options_.hp_filter == 0
b1 = b1*cs;
b2(:,exo_names_orig_ord) = ghu(iky,:);
b2 = b2*cs;
vx = lyapunov_symm(A,b1*b1',options_.qz_criterium,options_.lyapunov_complex_threshold,1,[],options_.debug);
vx = lyapunov_symm(A,b1*b1',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,1,[],options_.debug);
vv = diag(aa*vx*aa'+b2*b2');
vv2 = 0;
for i=1:M_.exo_nbr
vx1 = lyapunov_symm(A,b1(:,i)*b1(:,i)',options_.qz_criterium,options_.lyapunov_complex_threshold,2,[],options_.debug);
vx1 = lyapunov_symm(A,b1(:,i)*b1(:,i)',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,2,[],options_.debug);
vx2 = abs(diag(aa*vx1*aa'+b2(:,i)*b2(:,i)'));
Gamma_y{nar+2}(stationary_vars,i) = vx2;
vv2 = vv2 +vx2;

2
matlab/thet2tau.m
View File

@ -51,7 +51,7 @@ elseif flagmoments==-1
tau=[oo_.dr.ys(oo_.dr.order_var); g1(:)];
else
GAM = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
GAM = lyapunov_symm(A,B*M_.Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
k = find(abs(GAM) < 1e-12);
GAM(k) = 0;
if useautocorr,

2
tests/optimal_policy/mult_elimination_test.mod
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@ -60,7 +60,7 @@ V0 = oo_.var(k4,k4);
Atest = [dr2.M1(k3,:) dr2.M2(k3,:) dr2.M4(k3,:); eye(6) zeros(6,10);zeros(4,16)];
Btest = [dr2.M3(k3,:); zeros(6,4); eye(4)];
V1=lyapunov_symm(Atest,Btest*M_.Sigma_e*Btest',1+1e-6,options_.lyapunov_complex_threshold);
V1=lyapunov_symm(Atest,Btest*M_.Sigma_e*Btest',options_.lyapunov_fixed_point_tol,1+1e-6,options_.lyapunov_complex_threshold);
if max(max(abs(V1(1:6,1:6)-V0)))
disp('Test OK')