206 lines
7.4 KiB
Matlab
206 lines
7.4 KiB
Matlab
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function [dr,info,M_,options_,oo_] = stochastic_solvers(dr,task,M_,options_,oo_)
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% function [dr,info,M_,options_,oo_] = stochastic_solvers(dr,task,M_,options_,oo_)
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% computes the reduced form solution of a rational expectation model (first or second order
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% approximation of the stochastic model around the deterministic steady state).
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%
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% INPUTS
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% dr [matlab structure] Decision rules for stochastic simulations.
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% task [integer] if task = 0 then dr1 computes decision rules.
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% if task = 1 then dr1 computes eigenvalues.
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% M_ [matlab structure] Definition of the model.
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% options_ [matlab structure] Global options.
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% oo_ [matlab structure] Results
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%
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% OUTPUTS
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% dr [matlab structure] Decision rules for stochastic simulations.
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% info [integer] info=1: the model doesn't define current variables uniquely
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% info=2: problem in mjdgges.dll info(2) contains error code.
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% info=3: BK order condition not satisfied info(2) contains "distance"
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% absence of stable trajectory.
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% info=4: BK order condition not satisfied info(2) contains "distance"
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% indeterminacy.
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% info=5: BK rank condition not satisfied.
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% info=6: The jacobian matrix evaluated at the steady state is complex.
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% M_ [matlab structure]
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% options_ [matlab structure]
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% oo_ [matlab structure]
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%
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% ALGORITHM
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% ...
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%
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% SPECIAL REQUIREMENTS
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% none.
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%
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% Copyright (C) 1996-2009 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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if (options_.aim_solver == 1) && (options_.order > 1)
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error('Option "aim_solver" is incompatible with order >= 2')
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end
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if options_.k_order_solver;
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if options_.risky_steadystate
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[dr,info] = dyn_risky_steadystate_solver(oo_.steady_state,M_,dr, ...
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options_,oo_);
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else
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dr = set_state_space(dr,M_);
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[dr,info] = k_order_pert(dr,M_,options_,oo_);
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end
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return;
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end
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if options_.ramsey_policy
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% expanding system for Optimal Linear Regulator
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[jacobia_,dr,info,M_,oo_] = dyn_ramsey_linearized_foc(dr,M_,options_,oo_);
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else
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klen = M_.maximum_lag + M_.maximum_lead + 1;
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iyv = M_.lead_lag_incidence';
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iyv = iyv(:);
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iyr0 = find(iyv) ;
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it_ = M_.maximum_lag + 1 ;
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if M_.exo_nbr == 0
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oo_.exo_steady_state = [] ;
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end
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it_ = M_.maximum_lag + 1;
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z = repmat(dr.ys,1,klen);
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z = z(iyr0) ;
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if options_.order == 1
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[junk,jacobia_] = feval([M_.fname '_dynamic'],z,[oo_.exo_simul ...
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oo_.exo_det_simul], M_.params, dr.ys, it_);
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elseif options_.order == 2
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[junk,jacobia_,hessian1] = feval([M_.fname '_dynamic'],z,...
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[oo_.exo_simul ...
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oo_.exo_det_simul], M_.params, dr.ys, it_);
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if options_.use_dll
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% In USE_DLL mode, the hessian is in the 3-column sparse representation
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hessian1 = sparse(hessian1(:,1), hessian1(:,2), hessian1(:,3), ...
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size(jacobia_, 1), size(jacobia_, 2)*size(jacobia_, 2));
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end
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end
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end
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if options_.debug
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save([M_.fname '_debug.mat'],'jacobia_')
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end
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if ~isreal(jacobia_)
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if max(max(abs(imag(jacobia_)))) < 1e-15
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jacobia_ = real(jacobia_);
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else
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info(1) = 6;
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info(2) = sum(sum(imag(jacobia_).^2));
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return
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end
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end
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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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nz = nnz(M_.lead_lag_incidence);
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sdyn = M_.endo_nbr - nstatic;
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[junk,cols_b,cols_j] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+1, ...
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order_var));
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b = zeros(M_.endo_nbr,M_.endo_nbr);
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b(:,cols_b) = jacobia_(:,cols_j);
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if M_.maximum_endo_lead == 0
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% backward models: simplified code exist only at order == 1
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% If required, use AIM solver if not check only
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if options_.order == 1
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[k1,junk,k2] = find(kstate(:,4));
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temp = -b\jacobia_(:,[k2 nz+1:end]);
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dr.ghx = temp(:,1:npred);
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if M_.exo_nbr
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dr.ghu = temp(:,npred+1:end);
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end
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dr.eigval = eig(transition_matrix(dr));
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dr.rank = 0;
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if any(abs(dr.eigval) > options_.qz_criterium)
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temp = sort(abs(dr.eigval));
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nba = nnz(abs(dr.eigval) > options_.qz_criterium);
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temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
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info(1) = 3;
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info(2) = temp'*temp;
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end
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else
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error(['2nd and 3rd order approximation not implemented for purely ' ...
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'backward models'])
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end
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elseif M_.maximum_endo_lag == 0
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% purely forward model
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dr.ghx = [];
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dr.ghu = -b\jacobia_(:,nz+1:end);
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elseif options_.risky_steadystate
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[dr,info] = dyn_risky_steadystate_solver(oo_.steady_state,M_,dr, ...
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options_,oo_);
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else
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% If required, use AIM solver if not check only
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if (options_.aim_solver == 1) && (task == 0)
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[dr,info] = AIM_first_order_solver(jacobia_,M_,dr,sdim);
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else % use original Dynare solver
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[dr,info] = dyn_first_order_solver(jacobia_,b,M_,dr,options_,task);
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if info
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return;
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end
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end
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if options_.loglinear == 1
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k = find(dr.kstate(:,2) <= M_.maximum_endo_lag+1);
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klag = dr.kstate(k,[1 2]);
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k1 = dr.order_var;
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dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
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repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
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dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
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end
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%exogenous deterministic variables
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if M_.exo_det_nbr > 0
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f1 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+2:end,order_var))));
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f0 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var))));
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fudet = sparse(jacobia_(:,nz+M_.exo_nbr+1:end));
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M1 = inv(f0+[zeros(M_.endo_nbr,nstatic) f1*gx zeros(M_.endo_nbr,nyf-nboth)]);
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M2 = M1*f1;
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dr.ghud = cell(M_.exo_det_length,1);
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dr.ghud{1} = -M1*fudet;
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for i = 2:M_.exo_det_length
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dr.ghud{i} = -M2*dr.ghud{i-1}(end-nyf+1:end,:);
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end
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end
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if options_.order > 1
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% Second order
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dr = dyn_second_order_solver(jacobia_,hessian1,dr,M_,...
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options_.threads.kronecker.A_times_B_kronecker_C,...
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options_.threads.kronecker.sparse_hessian_times_B_kronecker_C);
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end
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end
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oo.dr = dr;
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