213 lines
6.4 KiB
Matlab
213 lines
6.4 KiB
Matlab
function oo_ = sim1_linear(options_, M_, oo_)
|
|
|
|
% Solves a linear approximation of a perfect foresight model susing sparse matrix.
|
|
%
|
|
% INPUTS
|
|
% - options_ [struct] contains various options.
|
|
% - M_ [struct] contains a description of the model.
|
|
% - oo_ [struct] contains results.
|
|
%
|
|
% OUTPUTS
|
|
% - oo_
|
|
|
|
% Copyright (C) 2015 Dynare Team
|
|
%
|
|
% This file is part of Dynare.
|
|
%
|
|
% Dynare is free software: you can redistribute it and/or modify
|
|
% it under the terms of the GNU General Public License as published by
|
|
% the Free Software Foundation, either version 3 of the License, or
|
|
% (at your option) any later version.
|
|
%
|
|
% Dynare is distributed in the hope that it will be useful,
|
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
% GNU General Public License for more details.
|
|
%
|
|
% You should have received a copy of the GNU General Public License
|
|
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
|
|
|
verbose = options_.verbosity;
|
|
|
|
lead_lag_incidence = M_.lead_lag_incidence;
|
|
|
|
ny = M_.endo_nbr;
|
|
nx = M_.exo_nbr;
|
|
|
|
maximum_lag = M_.maximum_lag;
|
|
max_lag = M_.maximum_endo_lag;
|
|
|
|
nyp = nnz(lead_lag_incidence(1,:)) ;
|
|
ny0 = nnz(lead_lag_incidence(2,:)) ;
|
|
nyf = nnz(lead_lag_incidence(3,:)) ;
|
|
|
|
nd = nyp+ny0+nyf; % size of y (first argument passed to the dynamic file).
|
|
|
|
periods = options_.periods;
|
|
y_steady_state = oo_.steady_state;
|
|
x_steady_state = oo_.exo_steady_state;
|
|
|
|
params = M_.params;
|
|
endo_simul = oo_.endo_simul;
|
|
exo_simul = oo_.exo_simul;
|
|
|
|
% Indices in A.
|
|
ip = find(lead_lag_incidence(1,:)');
|
|
ic = find(lead_lag_incidence(2,:)');
|
|
in = find(lead_lag_incidence(3,:)');
|
|
icn = find(lead_lag_incidence(2:3,:)');
|
|
ipcn = find(lead_lag_incidence');
|
|
|
|
% Indices in y.
|
|
jp = nonzeros(lead_lag_incidence(1,:)');
|
|
jc = nonzeros(lead_lag_incidence(2,:)');
|
|
jn = nonzeros(lead_lag_incidence(3,:)');
|
|
jpc = [jp; jc];
|
|
jcn = [jc; jn];
|
|
|
|
jexog = transpose(nd+(1:nx));
|
|
jendo = transpose(1:nd);
|
|
|
|
i_upd = maximum_lag*ny+(1:periods*ny);
|
|
|
|
% Center the endogenous and exogenous variables around the deterministic steady state.
|
|
endo_simul = bsxfun(@minus,endo_simul,y_steady_state);
|
|
exo_simul =bsxfun(@minus,exo_simul,transpose(x_steady_state));
|
|
|
|
Y = endo_simul(:);
|
|
|
|
if verbose
|
|
skipline()
|
|
printline(80)
|
|
disp('MODEL SIMULATION:')
|
|
skipline()
|
|
end
|
|
|
|
model_dynamic = str2func([M_.fname,'_dynamic']);
|
|
z = y_steady_state([ip; ic; in]);
|
|
|
|
% Evaluate the Jacobian of the dynamic model at the deterministic steady state.
|
|
[d1,jacobian] = model_dynamic(z,transpose(x_steady_state), params, y_steady_state,1);
|
|
|
|
% Check that the dynamic model was evaluated at the steady state.
|
|
if max(abs(d1))>1e-12
|
|
error('Jacobian is not evaluated at the steady state!')
|
|
end
|
|
|
|
[rT,cT,vT] = find(jacobian(:,jpc));
|
|
[r1,c1,v1] = find(jacobian(:,jcn));
|
|
[rr,cc,vv] = find(jacobian(:,jendo));
|
|
|
|
ivT = 1:length(vT);
|
|
iv1 = 1:length(v1);
|
|
iv = 1:length(vv);
|
|
|
|
% Initialize the vector of residuals.
|
|
res = zeros(periods*ny,1);
|
|
|
|
% Initialize the sparse Jacobian.
|
|
iA = zeros(periods*M_.NNZDerivatives(1),3);
|
|
|
|
h2 = clock ;
|
|
i_rows = (1:ny)';
|
|
i_cols_A = ipcn;
|
|
i_cols = ipcn+(maximum_lag-1)*ny;
|
|
m = 0;
|
|
for it = (maximum_lag+1):(maximum_lag+periods)
|
|
if it == maximum_lag+periods
|
|
nv = length(vT);
|
|
iA(ivT+m,:) = [i_rows(rT),i_cols_A(jpc(cT)),vT];
|
|
elseif it == maximum_lag+1
|
|
nv = length(v1);
|
|
iA(iv1+m,:) = [i_rows(r1),icn(c1),v1];
|
|
else
|
|
nv = length(vv);
|
|
iA(iv+m,:) = [i_rows(rr),i_cols_A(cc),vv];
|
|
end
|
|
z(jendo) = Y(i_cols);
|
|
z(jexog) = transpose(exo_simul(it,:));
|
|
res(i_rows) = jacobian*z;
|
|
m = m + nv;
|
|
i_rows = i_rows + ny;
|
|
i_cols = i_cols + ny;
|
|
if it > maximum_lag+1
|
|
i_cols_A = i_cols_A + ny;
|
|
end
|
|
end
|
|
|
|
% Evaluation of the maximum residual at the initial guess (steady state for the endogenous variables).
|
|
err = max(abs(res));
|
|
|
|
if options_.debug
|
|
fprintf('\nLargest absolute residual at iteration %d: %10.3f\n',1,err);
|
|
if any(isnan(res)) || any(isinf(res)) || any(isnan(Y)) || any(isinf(Y))
|
|
fprintf('\nWARNING: NaN or Inf detected in the residuals or endogenous variables.\n');
|
|
end
|
|
if ~isreal(res) || ~isreal(Y)
|
|
fprintf('\nWARNING: Imaginary parts detected in the residuals or endogenous variables.\n');
|
|
end
|
|
skipline()
|
|
end
|
|
|
|
iA = iA(1:m,:);
|
|
A = sparse(iA(:,1),iA(:,2),iA(:,3),periods*ny,periods*ny);
|
|
|
|
% Try to update the vector of endogenous variables.
|
|
try
|
|
Y(i_upd) = Y(i_upd) - A\res;
|
|
catch
|
|
% Normally, because the model is linear, the solution of the perfect foresight model should
|
|
% be obtained in one Newton step. This is not the case if the model is singular.
|
|
oo_.deterministic_simulation.status = false;
|
|
oo_.deterministic_simulation.error = NaN;
|
|
oo_.deterministic_simulation.iterations = 1;
|
|
if verbose
|
|
skipline()
|
|
disp('Singularity problem! The jacobian matrix of the stacked model cannot be inverted.')
|
|
end
|
|
return
|
|
end
|
|
|
|
i_cols = ipcn+(maximum_lag-1)*ny;
|
|
i_rows = (1:ny)';
|
|
for it = (maximum_lag+1):(maximum_lag+periods)
|
|
z(jendo) = Y(i_cols);
|
|
z(jexog) = transpose(exo_simul(it,:));
|
|
m = m + nv;
|
|
res(i_rows) = jacobian*z;
|
|
i_rows = i_rows + ny;
|
|
i_cols = i_cols + ny;
|
|
end
|
|
|
|
ERR = max(abs(res));
|
|
|
|
if verbose
|
|
fprintf('Iter: %s,\t Initial err. = %s,\t err. = %s,\t time = %s\n',num2str(1),num2str(err),num2str(ERR), num2str(etime(clock,h2)));
|
|
printline(80);
|
|
end
|
|
|
|
if any(isnan(res)) || any(isinf(res)) || any(isnan(Y)) || any(isinf(Y)) || ~isreal(res) || ~isreal(Y)
|
|
oo_.deterministic_simulation.status = false;% NaN or Inf occurred
|
|
oo_.deterministic_simulation.error = ERR;
|
|
oo_.deterministic_simulation.iterations = 1;
|
|
oo_.endo_simul = reshape(Y,ny,periods+maximum_lag+M_.maximum_lead);
|
|
if verbose
|
|
skipline()
|
|
if ~isreal(res) || ~isreal(Y)
|
|
disp('Simulation terminated with imaginary parts in the residuals or endogenous variables.')
|
|
else
|
|
disp('Simulation terminated with NaN or Inf in the residuals or endogenous variables.')
|
|
end
|
|
disp('There is most likely something wrong with your model. Try model_diagnostics or another simulation method.')
|
|
end
|
|
else
|
|
oo_.deterministic_simulation.status = true;% Convergency obtained.
|
|
oo_.deterministic_simulation.error = ERR;
|
|
oo_.deterministic_simulation.iterations = 1;
|
|
oo_.endo_simul = bsxfun(@plus,reshape(Y,ny,periods+maximum_lag+M_.maximum_lead),y_steady_state);
|
|
end
|
|
|
|
if verbose
|
|
skipline();
|
|
end
|