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function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model(endo_simul,exo_simul,pfm,nnodes,order)
% Copyright (C) 2012 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/>.
flag = 0;
err = 0;
stop = 0;
params = pfm.params;
steady_state = pfm.steady_state;
ny = pfm.ny;
periods = pfm.periods;
dynamic_model = pfm.dynamic_model;
lead_lag_incidence = pfm.lead_lag_incidence;
nyp = pfm.nyp;
nyf = pfm.nyf;
i_cols_1 = pfm.i_cols_1;
i_cols_A1 = pfm.i_cols_A1;
i_cols_j = pfm.i_cols_j;
i_cols_T = nonzeros(lead_lag_incidence(1:2,:)');
maxit = pfm.maxit_;
tolerance = pfm.tolerance;
verbose = pfm.verbose;
number_of_shocks = size(exo_simul,2);
[nodes,weights] = gauss_hermite_weights_and_nodes(nnodes);
if number_of_shocks>1
nodes = repmat(nodes,1,number_of_shocks)*chol(pfm.Sigma_e);
% to be fixed for Sigma ~= I
for i=1:number_of_shocks
rr(i) = {nodes(:,i)};
ww(i) = {weights};
end
nodes = cartesian_product_of_sets(rr{:});
weights = prod(cartesian_product_of_sets(ww{:}),2);
nnodes = nnodes^number_of_shocks;
else
nodes = nodes*sqrt(pfm.Sigma_e);
end
innovations = zeros(periods+2,number_of_shocks);
if verbose
disp ([' -----------------------------------------------------']);
disp (['MODEL SIMULATION :']);
fprintf('\n');
end
z = endo_simul(find(lead_lag_incidence'));
[d1,jacobian] = dynamic_model(z,exo_simul,params,steady_state,2);
% Each column of Y represents a different world
% The upper right cells are unused
% The first row block is ny x 1
% The second row block is ny x nnodes
% The third row block is ny x nnodes^2
% and so on until size ny x nnodes^order
world_nbr = nnodes^order;
Y = repmat(endo_simul(:),1,world_nbr);
% The columns of A map the elements of Y such that
% each block of Y with ny rows are unfolded column wise
dimension = ny*(sum(nnodes.^(0:order-1),2)+(periods-order)*world_nbr);
if order == 0
i_upd = ny+(1:ny*periods);
else
i_upd = zeros(dimension,1);
i_upd(1:ny) = ny+(1:ny);
i1 = ny+1;
i2 = 2*ny;
n1 = 2*ny+1;
n2 = 3*ny;
for i=2:periods
k = n1:n2;
for j=1:nnodes^min(i-1,order)
i_upd(i1:i2) = (n1:n2)+(j-1)*ny*(periods+2);
i1 = i2+1;
i2 = i2+ny;
end
n1 = n2+1;
n2 = n2+ny;
end
end
h1 = clock;
for iter = 1:maxit
h2 = clock;
A = sparse([],[],[],dimension,dimension,(periods+2)*world_nbr*nnz(jacobian));
res = zeros(dimension,1);
i_rows = 1:ny;
i_cols = find(lead_lag_incidence');
i_cols_p = i_cols(1:nyp);
i_cols_s = i_cols(nyp+(1:ny));
i_cols_f = i_cols(nyp+ny+(1:nyf));
i_cols_A = i_cols;
i_cols_Ap = i_cols_p;
i_cols_As = i_cols_s;
i_cols_Af = i_cols_f - ny;
for i = 1:periods
if i <= order+1
i_w_p = 1;
for j = 1:nnodes^(i-1)
innovation = exo_simul;
if i > 1
innovation(i+1,:) = nodes(mod(j-1,nnodes)+1,:);
end
if i <= order
for k=1:nnodes
y = [Y(i_cols_p,i_w_p);
Y(i_cols_s,j);
Y(i_cols_f,(j-1)*nnodes+k)];
[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
i_cols_A = [i_cols_As - ny; i_cols_Af];
A(i_rows,i_cols_A) = A(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A(i_rows,i_cols_A) = A(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_j);
end
res(i_rows) = res(i_rows)+weights(k)*d1;
i_cols_Af = i_cols_Af + ny;
end
else
y = [Y(i_cols_p,i_w_p);
Y(i_cols_s,j);
Y(i_cols_f,j)];
[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
i_cols_A = [i_cols_As - ny; i_cols_Af];
A(i_rows,i_cols_A) = jacobian(:,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A(i_rows,i_cols_A) = jacobian(:,i_cols_j);
end
res(i_rows) = d1;
i_cols_Af = i_cols_Af + ny;
end
i_rows = i_rows + ny;
if mod(j,nnodes) == 0
i_w_p = i_w_p + 1;
end
if i > 1
if mod(j,nnodes) == 0
i_cols_Ap = i_cols_Ap + ny;
end
i_cols_As = i_cols_As + ny;
end
end
i_cols_p = i_cols_p + ny;
i_cols_s = i_cols_s + ny;
i_cols_f = i_cols_f + ny;
elseif i == periods
if i == order+2
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
end
for j=1:world_nbr
[d1,jacobian] = dynamic_model(Y(i_cols,j),exo_simul, ...
params,steady_state,i+1);
A(i_rows,i_cols_A(i_cols_T)) = jacobian(:,i_cols_T);
res(i_rows) = d1;
i_rows = i_rows + ny;
i_cols_A = i_cols_A + ny;
end
else
if i == order+2
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
end
for j=1:world_nbr
[d1,jacobian] = dynamic_model(Y(i_cols,j), ...
exo_simul,params,steady_state,i+1);
A(i_rows,i_cols_A) = jacobian(:,i_cols_j);
res(i_rows) = d1;
i_rows = i_rows + ny;
i_cols_A = i_cols_A + ny;
end
end
i_cols = i_cols + ny;
end
err = max(abs(res));
if err < tolerance
stop = 1;
if verbose
fprintf('\n') ;
disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
fprintf('\n') ;
disp([' Convergency obtained.']) ;
fprintf('\n') ;
end
flag = 0;% Convergency obtained.
endo_simul = reshape(Y(:,1),ny,periods+2);%Y(ny+(1:ny),1);
% figure;plot(Y(16:ny:(periods+2)*ny,:))
% pause
break
end
dy = -A\res;
Y(i_upd) = Y(i_upd) + dy;
end
if ~stop
if verbose
fprintf('\n') ;
disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
fprintf('\n') ;
disp(['WARNING : maximum number of iterations is reached (modify options_.maxit_).']) ;
fprintf('\n') ;
end
flag = 1;% more iterations are needed.
endo_simul = 1;
end
if verbose
disp (['-----------------------------------------------------']) ;
end
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