333 lines
10 KiB
Matlab
333 lines
10 KiB
Matlab
function [endogenousvariables, info] = sim1(endogenousvariables, exogenousvariables, steadystate, M, options)
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% Performs deterministic simulations with lead or lag on one period. Uses sparse matrices.
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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 [double] N*1 array, steady state for the endogenous 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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% 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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% ALGORITHM
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% ...
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%
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% SPECIAL REQUIREMENTS
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% None.
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% Copyright (C) 1996-2018 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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endogenous_terminal_period = options.endogenous_terminal_period;
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vperiods = options.periods*ones(1,options.simul.maxit);
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azero = options.dynatol.f/1e7;
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lead_lag_incidence = M.lead_lag_incidence;
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ny = M.endo_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;
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stop = 0 ;
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periods = options.periods;
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params = M.params;
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i_cols_1 = nonzeros(lead_lag_incidence(2:3,:)');
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i_cols_A1 = find(lead_lag_incidence(2:3,:)');
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i_cols_A1 = i_cols_A1(:);
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i_cols_T = nonzeros(lead_lag_incidence(1:2,:)');
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i_cols_0 = nonzeros(lead_lag_incidence(2,:)');
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i_cols_A0 = find(lead_lag_incidence(2,:)');
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i_cols_A0 = i_cols_A0(:);
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i_cols_j = (1:nd)';
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i_upd = maximum_lag*ny+(1:periods*ny);
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Y = endogenousvariables(:);
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if verbose
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skipline()
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printline(56)
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disp('MODEL SIMULATION:')
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skipline()
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end
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model_dynamic = str2func([M.fname,'.dynamic']);
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z = Y(find(lead_lag_incidence'));
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[d1,jacobian] = model_dynamic(z, exogenousvariables, params, steadystate,maximum_lag+1);
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res = zeros(periods*ny,1);
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o_periods = periods;
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if endogenous_terminal_period
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ZERO = zeros(length(i_upd),1);
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end
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h1 = clock ;
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iA = zeros(periods*M.NNZDerivatives(1),3);
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for iter = 1:options.simul.maxit
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h2 = clock ;
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i_rows = (1:ny)';
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i_cols_A = find(lead_lag_incidence');
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i_cols_A = i_cols_A(:);
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i_cols = i_cols_A+(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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[d1,jacobian] = model_dynamic(Y(i_cols), exogenousvariables, params, steadystate,it);
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if it == maximum_lag+periods && it == maximum_lag+1
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[r,c,v] = find(jacobian(:,i_cols_0));
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iA((1:length(v))+m,:) = [i_rows(r(:)),i_cols_A0(c(:)),v(:)];
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elseif it == maximum_lag+periods
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[r,c,v] = find(jacobian(:,i_cols_T));
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iA((1:length(v))+m,:) = [i_rows(r(:)),i_cols_A(i_cols_T(c(:))),v(:)];
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elseif it == maximum_lag+1
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[r,c,v] = find(jacobian(:,i_cols_1));
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iA((1:length(v))+m,:) = [i_rows(r(:)),i_cols_A1(c(:)),v(:)];
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else
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[r,c,v] = find(jacobian(:,i_cols_j));
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iA((1:length(v))+m,:) = [i_rows(r(:)),i_cols_A(c(:)),v(:)];
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end
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m = m + length(v);
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res(i_rows) = d1;
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if endogenous_terminal_period && iter>1
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dr = max(abs(d1));
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if dr<azero
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vperiods(iter) = it;
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periods = it-maximum_lag+1;
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break
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end
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end
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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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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',iter,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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if verbose
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str = sprintf('Iter: %s,\t err. = %s, \t time = %s',num2str(iter),num2str(err), num2str(etime(clock,h2)));
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disp(str);
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end
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if err < options.dynatol.f
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stop = 1 ;
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break
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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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if endogenous_terminal_period && iter>1
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dy = ZERO;
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if options.simul.robust_lin_solve
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dy(1:i_rows(end)) = -lin_solve_robust( A(1:i_rows(end),1:i_rows(end)), res(1:i_rows(end)),verbose );
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else
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dy(1:i_rows(end)) = -lin_solve( A(1:i_rows(end),1:i_rows(end)), res(1:i_rows(end)), verbose );
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end
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else
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if options.simul.robust_lin_solve
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dy = -lin_solve_robust( A, res, verbose );
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else
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dy = -lin_solve( A, res, verbose );
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end
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end
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if any(~isreal(dy)) || any(isnan(dy)) || any(isinf(dy))
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if verbose
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display_critical_variables(reshape(dy,[ny periods])', M);
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end
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end
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Y(i_upd) = Y(i_upd) + dy;
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end
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if endogenous_terminal_period
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err = evaluate_max_dynamic_residual(model_dynamic, Y, exogenousvariables, params, steadystate, o_periods, ny, max_lag, lead_lag_incidence);
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periods = o_periods;
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end
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if stop
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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 = iter;
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info.periods = vperiods(1:iter);
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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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disp(sprintf('Total time of simulation: %s.', num2str(etime(clock,h1))))
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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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display_critical_variables(reshape(dy,[ny periods])', M);
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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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printline(105)
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end
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else
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if verbose
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skipline();
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disp(sprintf('Total time of simulation: %s', num2str(etime(clock,h1))))
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printline(56)
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end
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info.status = true;% Convergency obtained.
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info.error = err;
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info.iterations = iter;
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info.periods = vperiods(1:iter);
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endogenousvariables = reshape(Y,ny,periods+maximum_lag+M.maximum_lead);
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end
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elseif ~stop
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if verbose
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skipline();
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disp(sprintf('Total time of simulation: %s.', num2str(etime(clock,h1))))
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disp('Maximum number of iterations is reached (modify option maxit).')
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printline(62)
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end
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info.status = false;% more iterations are needed.
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info.error = err;
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info.periods = vperiods(1:iter);
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info.iterations = options.simul.maxit;
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end
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if verbose
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skipline();
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end
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function x = lin_solve( A, b,verbose)
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if norm( b ) < sqrt( eps ) % then x = 0 is a solution
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x = 0;
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return
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end
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x = A\b;
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x( ~isfinite( x ) ) = 0;
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relres = norm( b - A * x ) / norm( b );
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if relres > 1e-6 && verbose
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fprintf( 'WARNING : Failed to find a solution to the linear system.\n' );
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end
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function [ x, flag, relres ] = lin_solve_robust( A, b , verbose)
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if norm( b ) < sqrt( eps ) % then x = 0 is a solution
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x = 0;
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flag = 0;
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relres = 0;
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return
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end
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x = A\b;
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x( ~isfinite( x ) ) = 0;
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[ x, flag, relres ] = bicgstab( A, b, [], [], [], [], x ); % returns immediately if x is a solution
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if flag == 0
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return
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end
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disp( relres );
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if verbose
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fprintf( 'Initial bicgstab failed, trying alternative start point.\n' );
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end
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old_x = x;
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old_relres = relres;
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[ x, flag, relres ] = bicgstab( A, b );
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if flag == 0
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return
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end
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if verbose
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fprintf( 'Alternative start point also failed with bicgstab, trying gmres.\n' );
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end
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if old_relres < relres
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x = old_x;
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end
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[ x, flag, relres ] = gmres( A, b, [], [], [], [], [], x );
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if flag == 0
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return
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end
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if verbose
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fprintf( 'Initial gmres failed, trying alternative start point.\n' );
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end
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old_x = x;
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old_relres = relres;
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[ x, flag, relres ] = gmres( A, b );
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if flag == 0
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return
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end
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if verbose
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fprintf( 'Alternative start point also failed with gmres, using the (SLOW) Moore-Penrose Pseudo-Inverse.\n' );
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end
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if old_relres < relres
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x = old_x;
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relres = old_relres;
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end
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old_x = x;
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old_relres = relres;
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x = pinv( full( A ) ) * b;
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relres = norm( b - A * x ) / norm( b );
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if old_relres < relres
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x = old_x;
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relres = old_relres;
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end
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flag = relres > 1e-6;
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if flag ~= 0 && verbose
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fprintf( 'WARNING : Failed to find a solution to the linear system\n' );
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end
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function display_critical_variables(dyy, M)
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if any(isnan(dyy))
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indx = find(any(isnan(dyy)));
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endo_names= M.endo_names(indx);
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disp('Last iteration provided NaN for the following variables:')
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fprintf('%s, ', endo_names{:}),
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fprintf('\n'),
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end
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if any(isinf(dyy))
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indx = find(any(isinf(dyy)));
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endo_names = M.endo_names(indx);
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disp('Last iteration diverged (Inf) for the following variables:')
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fprintf('%s, ', endo_names{:}),
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fprintf('\n'),
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end
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if any(~isreal(dyy))
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indx = find(any(~isreal(dyy)));
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endo_names = M.endo_names(indx);
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disp('Last iteration provided complex number for the following variables:')
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fprintf('%s, ', endo_names{:}),
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fprintf('\n'),
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end |