236 lines
6.9 KiB
Matlab
236 lines
6.9 KiB
Matlab
function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
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%@info:
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%! @deftypefn {Function File} {[@var{dr},@var{info}] =} dyn_first_order_solver (@var{jacobia},@var{M_},@var{dr},@var{options},@var{task})
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%! @anchor{dyn_first_order_solver}
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%! @sp 1
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%! Computes the first order reduced form of the DSGE model
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%! @sp 2
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%! @strong{Inputs}
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%! @sp 1
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%! @table @ @var
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%! @item jacobia
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%! Matrix containing the Jacobian of the model
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%! @item M_
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%! Matlab's structure describing the model (initialized by @code{dynare}).
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%! @item dr
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%! Matlab's structure describing the reduced form solution of the model.
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%! @item qz_criterium
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%! Double containing the criterium to separate explosive from stable eigenvalues
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%! @end table
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%! @sp 2
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%! @strong{Outputs}
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%! @sp 1
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%! @table @ @var
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%! @item dr
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%! Matlab's structure describing the reduced form solution of the model.
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%! @item info
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%! Integer scalar, error code.
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%! @sp 1
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%! @table @ @code
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%! @item info==0
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%! No error.
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%! @item info==1
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%! The model doesn't determine the current variables uniquely.
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%! @item info==2
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%! MJDGGES returned an error code.
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%! @item info==3
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%! Blanchard & Kahn conditions are not satisfied: no stable equilibrium.
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%! @item info==4
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%! Blanchard & Kahn conditions are not satisfied: indeterminacy.
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%! @item info==5
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%! Blanchard & Kahn conditions are not satisfied: indeterminacy due to rank failure.
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%! @item info==7
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%! One of the generalized eigenvalues is close to 0/0
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%! @end table
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%! @end table
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%! @end deftypefn
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%@eod:
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% Copyright (C) 2001-2011 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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info = 0;
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dr.ghx = [];
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dr.ghu = [];
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klen = M_.maximum_endo_lag+M_.maximum_endo_lead+1;
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kstate = dr.kstate;
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kad = dr.kad;
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kae = dr.kae;
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nstatic = dr.nstatic;
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nfwrd = dr.nfwrd;
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npred = dr.npred;
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nboth = dr.nboth;
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order_var = dr.order_var;
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nd = size(kstate,1);
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lead_lag_incidence = M_.lead_lag_incidence;
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nz = nnz(lead_lag_incidence);
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sdyn = M_.endo_nbr - nstatic;
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[junk,cols_b,cols_j] = find(lead_lag_incidence(M_.maximum_endo_lag+1,...
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order_var));
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if nstatic > 0
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[Q,R] = qr(jacobia(:,cols_j(1:nstatic)));
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aa = Q'*jacobia;
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else
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aa = jacobia;
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end
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k1 = find([1:klen] ~= M_.maximum_endo_lag+1);
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a = aa(:,nonzeros(lead_lag_incidence(k1,:)'));
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b(:,cols_b) = aa(:,cols_j);
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b10 = b(1:nstatic,1:nstatic);
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b11 = b(1:nstatic,nstatic+1:end);
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b2 = b(nstatic+1:end,nstatic+1:end);
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if any(isinf(a(:)))
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info = 1;
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return
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end
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% buildind D and E
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d = zeros(nd,nd) ;
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e = d ;
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k = find(kstate(:,2) >= M_.maximum_endo_lag+2 & kstate(:,3));
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d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
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k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
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e(1:sdyn,k1) = -b2(:,kstate(k1,1)-nstatic);
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k = find(kstate(:,2) <= M_.maximum_endo_lag+1 & kstate(:,4));
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e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
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k2 = find(kstate(:,2) == M_.maximum_endo_lag+1);
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k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
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d(1:sdyn,k2) = b2(:,kstate(k2,1)-nstatic);
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if ~isempty(kad)
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for j = 1:size(kad,1)
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d(sdyn+j,kad(j)) = 1 ;
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e(sdyn+j,kae(j)) = 1 ;
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end
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end
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% 1) if mjdgges.dll (or .mexw32 or ....) doesn't exit,
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% matlab/qz is added to the path. There exists now qz/mjdgges.m that
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% contains the calls to the old Sims code
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% 2) In global_initialization.m, if mjdgges.m is visible exist(...)==2,
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% this means that the DLL isn't avaiable and use_qzdiv is set to 1
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[err,ss,tt,w,sdim,dr.eigval,info1] = mjdgges(e,d,options.qz_criterium);
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mexErrCheck('mjdgges', err);
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if info1
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if info1 == -30
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% one eigenvalue is close to 0/0
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info(1) = 7;
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else
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info(1) = 2;
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info(2) = info1;
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info(3) = size(e,2);
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end
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return
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end
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nba = nd-sdim;
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nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
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if task == 1
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dr.rank = rank(w(1:nyf,nd-nyf+1:end));
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% Under Octave, eig(A,B) doesn't exist, and
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% lambda = qz(A,B) won't return infinite eigenvalues
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if ~exist('OCTAVE_VERSION')
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dr.eigval = eig(e,d);
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end
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return
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end
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if nba ~= nyf
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temp = sort(abs(dr.eigval));
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if nba > nyf
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temp = temp(nd-nba+1:nd-nyf)-1-options.qz_criterium;
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info(1) = 3;
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elseif nba < nyf;
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temp = temp(nd-nyf+1:nd-nba)-1-options.qz_criterium;
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info(1) = 4;
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end
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info(2) = temp'*temp;
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return
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end
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np = nd - nyf;
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n2 = np + 1;
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n3 = nyf;
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n4 = n3 + 1;
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% derivatives with respect to dynamic state variables
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% forward variables
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w1 =w(1:n3,n2:nd);
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if ~isscalar(w1) && (condest(w1) > 1e9);
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% condest() fails on a scalar under Octave
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info(1) = 5;
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info(2) = condest(w1);
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return;
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else
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gx = -w1'\w(n4:nd,n2:nd)';
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end
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% predetermined variables
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hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
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hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);
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k1 = find(kstate(n4:nd,2) == M_.maximum_endo_lag+1);
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k2 = find(kstate(1:n3,2) == M_.maximum_endo_lag+2);
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dr.gx = gx;
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dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
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%lead variables actually present in the model
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j3 = nonzeros(kstate(:,3));
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j4 = find(kstate(:,3));
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% derivatives with respect to exogenous variables
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if M_.exo_nbr
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fu = aa(:,nz+(1:M_.exo_nbr));
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a1 = b;
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aa1 = [];
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if nstatic > 0
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aa1 = a1(:,1:nstatic);
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end
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dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
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npred) a1(:,nstatic+npred+1:end)]\fu;
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else
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dr.ghu = [];
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end
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% static variables
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if nstatic > 0
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temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
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j5 = find(kstate(n4:nd,4));
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temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
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temp = b10\(temp-b11*dr.ghx);
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dr.ghx = [temp; dr.ghx];
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temp = [];
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end
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if options.use_qzdiv
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%% Necessary when using Sims' routines for QZ
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gx = real(gx);
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hx = real(hx);
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dr.ghx = real(dr.ghx);
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dr.ghu = real(dr.ghu);
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end
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dr.Gy = hx; |