183 lines
6.1 KiB
Matlab
183 lines
6.1 KiB
Matlab
function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_BC)
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%@info:
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%! @deftypefn {Function File} {@var{dr} =} dyn_second_order_solver (@var{jacobia},@var{hessian},@var{dr},@var{M_},@var{threads_ABC},@var{threads_BC})
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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 hessian
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%! Matrix containing the second order derivatives of the model
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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 M_
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%! Matlab's structure describing the model (initialized by @code{dynare}).
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%! @item threads_ABC
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%! Integer controlling number of threads in A_times_B_kronecker_C
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%! @item threads_BC
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%! Integer controlling number of threads in sparse_hessian_times_B_kronecker_C
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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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%! @end table
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%! @end deftypefn
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%@eod:
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% Copyright (C) 2001-2012 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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dr.ghxx = [];
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dr.ghuu = [];
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dr.ghxu = [];
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dr.ghs2 = [];
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Gy = dr.Gy;
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kstate = dr.kstate;
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nstatic = M_.nstatic;
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nfwrd = M_.nfwrd;
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nspred = M_.nspred;
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nboth = M_.nboth;
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nsfwrd = M_.nsfwrd;
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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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np = nd - nsfwrd;
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k1 = nonzeros(lead_lag_incidence(:,order_var)');
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kk = [k1; length(k1)+(1:M_.exo_nbr+M_.exo_det_nbr)'];
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nk = size(kk,1);
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kk1 = reshape([1:nk^2],nk,nk);
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kk1 = kk1(kk,kk);
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% reordering second order derivatives
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hessian = hessian(:,kk1(:));
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zx = zeros(np,np);
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zu=zeros(np,M_.exo_nbr);
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zx(1:np,:)=eye(np);
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k0 = [1:M_.endo_nbr];
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gx1 = dr.ghx;
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hu = dr.ghu(nstatic+[1:nspred],:);
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k0 = find(lead_lag_incidence(M_.maximum_endo_lag+1,order_var)');
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zx = [zx; gx1(k0,:)];
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zu = [zu; dr.ghu(k0,:)];
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k1 = find(lead_lag_incidence(M_.maximum_endo_lag+2,order_var)');
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zu = [zu; gx1(k1,:)*hu];
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zx = [zx; gx1(k1,:)*Gy];
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zx=[zx; zeros(M_.exo_nbr,np);zeros(M_.exo_det_nbr,np)];
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zu=[zu; eye(M_.exo_nbr);zeros(M_.exo_det_nbr,M_.exo_nbr)];
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[nrzx,nczx] = size(zx);
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[rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zx,threads_BC);
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mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
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rhs = -rhs;
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%lhs
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n = M_.endo_nbr+sum(kstate(:,2) > M_.maximum_endo_lag+1 & kstate(:,2) < M_.maximum_endo_lag+M_.maximum_endo_lead+1);
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A = zeros(M_.endo_nbr,M_.endo_nbr);
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B = zeros(M_.endo_nbr,M_.endo_nbr);
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A(:,k0) = jacobia(:,nonzeros(lead_lag_incidence(M_.maximum_endo_lag+1,order_var)));
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% variables with the highest lead
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k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
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% Jacobian with respect to the variables with the highest lead
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fyp = jacobia(:,kstate(k1,3)+nnz(M_.lead_lag_incidence(M_.maximum_endo_lag+1,:)));
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B(:,nstatic+M_.npred+1:end) = fyp;
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[junk,k1,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+M_.maximum_endo_lead+1,order_var));
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A(1:M_.endo_nbr,nstatic+1:nstatic+nspred)=...
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A(1:M_.endo_nbr,nstatic+[1:nspred])+fyp*gx1(k1,1:nspred);
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C = Gy;
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D = [rhs; zeros(n-M_.endo_nbr,size(rhs,2))];
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[err, dr.ghxx] = gensylv(2,A,B,C,D);
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mexErrCheck('gensylv', err);
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%ghxu
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%rhs
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hu = dr.ghu(nstatic+1:nstatic+nspred,:);
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[rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zx,zu,threads_BC);
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mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
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hu1 = [hu;zeros(np-nspred,M_.exo_nbr)];
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[nrhx,nchx] = size(Gy);
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[nrhu1,nchu1] = size(hu1);
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[abcOut,err] = A_times_B_kronecker_C(dr.ghxx,Gy,hu1,threads_ABC);
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mexErrCheck('A_times_B_kronecker_C', err);
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B1 = B*abcOut;
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rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
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%lhs
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dr.ghxu = A\rhs;
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%ghuu
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%rhs
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[rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zu,threads_BC);
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mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
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[B1, err] = A_times_B_kronecker_C(B*dr.ghxx,hu1,threads_ABC);
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mexErrCheck('A_times_B_kronecker_C', err);
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rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
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%lhs
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dr.ghuu = A\rhs;
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% dr.ghs2
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% derivatives of F with respect to forward variables
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% reordering predetermined variables in diminishing lag order
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O1 = zeros(M_.endo_nbr,nstatic);
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O2 = zeros(M_.endo_nbr,M_.endo_nbr-nstatic-nspred);
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LHS = zeros(M_.endo_nbr,M_.endo_nbr);
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LHS(:,k0) = jacobia(:,nonzeros(lead_lag_incidence(M_.maximum_endo_lag+1,order_var)));
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RHS = zeros(M_.endo_nbr,M_.exo_nbr^2);
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gu = dr.ghu;
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guu = dr.ghuu;
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E = eye(M_.endo_nbr);
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kh = reshape([1:nk^2],nk,nk);
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kp = sum(kstate(:,2) <= M_.maximum_endo_lag+1);
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E1 = [eye(nspred); zeros(kp-nspred,nspred)];
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H = E1;
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hxx = dr.ghxx(nstatic+[1:nspred],:);
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[junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+2,order_var));
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k3 = nnz(M_.lead_lag_incidence(1:M_.maximum_endo_lag+1,:))+(1:M_.nsfwrd)';
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[B1, err] = sparse_hessian_times_B_kronecker_C(hessian(:,kh(k3,k3)),gu(k2a,:),threads_BC);
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mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
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RHS = RHS + jacobia(:,k2)*guu(k2a,:)+B1;
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% LHS
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LHS = LHS + jacobia(:,k2)*(E(k2a,:)+[O1(k2a,:) dr.ghx(k2a,:)*H O2(k2a,:)]);
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RHS = RHS*M_.Sigma_e(:);
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dr.fuu = RHS;
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%RHS = -RHS-dr.fbias;
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RHS = -RHS;
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dr.ghs2 = LHS\RHS;
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% deterministic exogenous variables
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if M_.exo_det_nbr > 0
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end
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