241 lines
7.9 KiB
Matlab
241 lines
7.9 KiB
Matlab
function [endogenousvariables, info] = sim1_linear(endogenousvariables, exogenousvariables, steadystate_y, steadystate_x, M, options)
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% Solves a linear approximation of a perfect foresight model using sparse matrix.
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%
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% INPUTS
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% - endogenousvariables [double] N*T array, paths for the endogenous variables (initial guess).
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% - exogenousvariables [double] T*M array, paths for the exogenous variables.
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% - steadystate_y [double] N*1 array, steady state for the endogenous variables.
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% - steadystate_x [double] M*1 array, steady state for the exogenous variables.
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% - M [struct] contains a description of the model.
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% - options [struct] contains various options.
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%
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% OUTPUTS
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% - endogenousvariables [double] N*T array, paths for the endogenous variables (solution of the perfect foresight model).
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% - info [struct] contains informations about the results.
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%
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% NOTATIONS
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% - N is the number of endogenous variables.
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% - M is the number of innovations.
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% - T is the number of periods (including initial and/or terminal conditions).
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%
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% REMARKS
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% - The structure `M` describing the structure of the model, must contain the
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% following informations:
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% + lead_lag_incidence, incidence matrix (given by the preprocessor).
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% + endo_nbr, number of endogenous variables (including aux. variables).
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% + exo_nbr, number of innovations.
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% + maximum_lag,
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% + maximum_endo_lag,
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% + params, values of model's parameters.
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% + fname, name of the model.
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% + NNZDerivatives, number of non zero elements in the jacobian of the dynamic model.
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% - The structure `options`, must contain the following options:
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% + verbosity, controls the quantity of information displayed.
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% + periods, the number of periods in the perfect foresight model.
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% + debug.
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% - The steady state of the exogenous variables is required because we need
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% to center the variables around the deterministic steady state to solve the
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% perfect foresight model.
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% Copyright (C) 2015-2017 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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verbose = options.verbosity;
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lead_lag_incidence = M.lead_lag_incidence;
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ny = M.endo_nbr;
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nx = M.exo_nbr;
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maximum_lag = M.maximum_lag;
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max_lag = M.maximum_endo_lag;
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nyp = nnz(lead_lag_incidence(1,:));
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ny0 = nnz(lead_lag_incidence(2,:));
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nyf = nnz(lead_lag_incidence(3,:));
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nd = nyp+ny0+nyf; % size of y (first argument passed to the dynamic file).
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periods = options.periods;
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params = M.params;
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% Indices in A.
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ip = find(lead_lag_incidence(1,:)');
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ic = find(lead_lag_incidence(2,:)');
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in = find(lead_lag_incidence(3,:)');
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icn = find(lead_lag_incidence(2:3,:)');
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ipcn = find(lead_lag_incidence');
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% Indices in y.
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jp = nonzeros(lead_lag_incidence(1,:)');
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jc = nonzeros(lead_lag_incidence(2,:)');
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jn = nonzeros(lead_lag_incidence(3,:)');
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jpc = [jp; jc];
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jcn = [jc; jn];
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jexog = transpose(nd+(1:nx));
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jendo = transpose(1:nd);
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i_upd = maximum_lag*ny+(1:periods*ny);
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% Center the endogenous and exogenous variables around the deterministic steady state.
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endogenousvariables = bsxfun(@minus, endogenousvariables, steadystate_y);
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exogenousvariables = bsxfun(@minus, exogenousvariables, transpose(steadystate_x));
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Y = endogenousvariables(:);
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if verbose
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skipline()
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printline(80)
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disp('MODEL SIMULATION:')
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skipline()
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end
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dynamicmodel = str2func([M.fname,'_dynamic']);
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z = steadystate_y([ip; ic; in]);
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% Evaluate the Jacobian of the dynamic model at the deterministic steady state.
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[d1,jacobian] = dynamicmodel(z, transpose(steadystate_x), params, steadystate_y, 1);
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% Check that the dynamic model was evaluated at the steady state.
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if max(abs(d1))>1e-12
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error('Jacobian is not evaluated at the steady state!')
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end
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[r0,c0,v0] = find(jacobian(:,jc));
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[rT,cT,vT] = find(jacobian(:,jpc));
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[r1,c1,v1] = find(jacobian(:,jcn));
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[rr,cc,vv] = find(jacobian(:,jendo));
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iv0 = 1:length(v0);
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ivT = 1:length(vT);
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iv1 = 1:length(v1);
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iv = 1:length(vv);
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% Initialize the vector of residuals.
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res = zeros(periods*ny, 1);
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% Initialize the sparse Jacobian.
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iA = zeros(periods*M.NNZDerivatives(1), 3);
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h2 = clock;
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i_rows = (1:ny)';
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i_cols_A = ipcn;
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i_cols = ipcn+(maximum_lag-1)*ny;
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m = 0;
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for it = (maximum_lag+1):(maximum_lag+periods)
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if isequal(it, maximum_lag+periods) && isequal(it, maximum_lag+1)
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nv = length(v0);
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iA(iv0+m,:) = [i_rows(r0),ic(c0),v0];
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elseif isequal(it, maximum_lag+periods)
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nv = length(vT);
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iA(ivT+m,:) = [i_rows(rT), i_cols_A(jpc(cT)), vT];
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elseif isequal(it, maximum_lag+1)
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nv = length(v1);
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iA(iv1+m,:) = [i_rows(r1), icn(c1), v1];
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else
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nv = length(vv);
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iA(iv+m,:) = [i_rows(rr),i_cols_A(cc),vv];
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end
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z(jendo) = Y(i_cols);
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z(jexog) = transpose(exogenousvariables(it,:));
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res(i_rows) = jacobian*z;
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m = m + nv;
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i_rows = i_rows + ny;
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i_cols = i_cols + ny;
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if it > maximum_lag+1
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i_cols_A = i_cols_A + ny;
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end
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end
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% Evaluation of the maximum residual at the initial guess (steady state for the endogenous variables).
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err = max(abs(res));
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if options.debug
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fprintf('\nLargest absolute residual at iteration %d: %10.3f\n', 1, err);
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if any(isnan(res)) || any(isinf(res)) || any(isnan(Y)) || any(isinf(Y))
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fprintf('\nWARNING: NaN or Inf detected in the residuals or endogenous variables.\n');
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end
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if ~isreal(res) || ~isreal(Y)
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fprintf('\nWARNING: Imaginary parts detected in the residuals or endogenous variables.\n');
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end
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skipline()
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end
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iA = iA(1:m,:);
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A = sparse(iA(:,1), iA(:,2), iA(:,3), periods*ny, periods*ny);
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% Try to update the vector of endogenous variables.
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try
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Y(i_upd) = Y(i_upd) - A\res;
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catch
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% Normally, because the model is linear, the solution of the perfect foresight model should
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% be obtained in one Newton step. This is not the case if the model is singular.
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info.status = false;
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info.error = NaN;
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info.iterations = 1;
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if verbose
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skipline()
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disp('Singularity problem! The jacobian matrix of the stacked model cannot be inverted.')
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end
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return
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end
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i_cols = ipcn+(maximum_lag-1)*ny;
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i_rows = (1:ny)';
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for it = (maximum_lag+1):(maximum_lag+periods)
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z(jendo) = Y(i_cols);
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z(jexog) = transpose(exogenousvariables(it,:));
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m = m + nv;
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res(i_rows) = jacobian*z;
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i_rows = i_rows + ny;
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i_cols = i_cols + ny;
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end
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ERR = max(abs(res));
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if verbose
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fprintf('Iter: %s,\t Initial err. = %s,\t err. = %s,\t time = %s\n', num2str(1), num2str(err), num2str(ERR), num2str(etime(clock,h2)));
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printline(80);
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end
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if any(isnan(res)) || any(isinf(res)) || any(isnan(Y)) || any(isinf(Y)) || ~isreal(res) || ~isreal(Y)
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info.status = false;% NaN or Inf occurred
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info.error = ERR;
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info.iterations = 1;
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endogenousvariables = reshape(Y, ny, periods+maximum_lag+M.maximum_lead);
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if verbose
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skipline()
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if ~isreal(res) || ~isreal(Y)
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disp('Simulation terminated with imaginary parts in the residuals or endogenous variables.')
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else
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disp('Simulation terminated with NaN or Inf in the residuals or endogenous variables.')
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end
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disp('There is most likely something wrong with your model. Try model_diagnostics or another simulation method.')
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end
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else
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info.status = true;% Convergency obtained.
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info.error = ERR;
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info.iterations = 1;
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endogenousvariables = bsxfun(@plus, reshape(Y, ny, periods+maximum_lag+M.maximum_lead), steadystate_y);
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end
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if verbose
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skipline();
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end |