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function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model_1(endo_simul,exo_simul,pfm,nnodes,order)
% Copyright (C) 2012-2013 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,:)');
hybrid_order = pfm.hybrid_order;
dr = pfm.dr;
maxit = pfm.maxit_;
tolerance = pfm.tolerance;
verbose = pfm.verbose;
number_of_shocks = size(exo_simul,2);
[nodes,weights] = gauss_hermite_weights_and_nodes(nnodes);
% make sure that there is a node equal to zero
% and permute nodes and weights to have zero first
k = find(abs(nodes) < 1e-12);
if ~isempty(k)
nodes = [nodes(k); nodes(1:k-1); nodes(k+1:end)];
weights = [weights(k); weights(1:k-1); weights(k+1:end)];
else
error('there is no nodes equal to zero')
end
if number_of_shocks>1
nodes = repmat(nodes,1,number_of_shocks)*chol(pfm.Sigma);
% 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);
end
if hybrid_order > 0
if hybrid_order == 2
h_correction = 0.5*dr.ghs2(dr.inv_order_var);
end
end
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 = 1+(nnodes-1)*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*(order+(nnodes-1)*(order-1)*order/2+(periods-order)*world_nbr);
if order == 0
i_upd_r = (1:ny*periods);
i_upd_y = i_upd_r + ny;
else
i_upd_r = zeros(dimension,1);
i_upd_y = i_upd_r;
i_upd_r(1:ny) = (1:ny);
i_upd_y(1:ny) = ny+(1:ny);
i1 = ny+1;
i2 = 2*ny;
n1 = ny+1;
n2 = 2*ny;
for i=2:periods
k = n1:n2;
for j=1:(1+(nnodes-1)*min(i-1,order))
i_upd_r(i1:i2) = (n1:n2)+(j-1)*ny*periods;
i_upd_y(i1:i2) = (n1:n2)+ny+(j-1)*ny*(periods+2);
i1 = i2+1;
i2 = i2+ny;
end
n1 = n2+1;
n2 = n2+ny;
end
end
icA = [find(lead_lag_incidence(1,:)) find(lead_lag_incidence(2,:))+world_nbr*ny ...
find(lead_lag_incidence(3,:))+2*world_nbr*ny]';
h1 = clock;
for iter = 1:maxit
h2 = clock;
A1 = sparse([],[],[],ny*(order+(nnodes-1)*(order-1)*order/2),dimension,(order+1)*world_nbr*nnz(jacobian));
res = zeros(ny,periods,world_nbr);
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_Ap0 = i_cols_p;
i_cols_As = i_cols_s;
i_cols_Af0 = i_cols_f - ny;
i_hc = i_cols_f - 2*ny;
for i = 1:order+1
i_w_p = 1;
for j = 1:(1+(nnodes-1)*(i-1))
innovation = exo_simul;
if i <= order && j == 1
% first world, integrating future shocks
for k=1:nnodes
if i == 2
i_cols_Ap = i_cols_Ap0;
elseif i > 2
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes- ...
1)*(i-2)*(i-3)/2);
end
if k == 1
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2);
else
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2+(i-1)*(nnodes-1) ...
+ k - 1);
end
if i > 1
innovation(i+1,:) = nodes(k,:);
end
if k == 1
k1 = 1;
else
k1 = (nnodes-1)*(i-1)+k;
end
if hybrid_order == 2 && (k > 1 || i == order)
y = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)+h_correction(i_hc)];
else
y = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)];
end
[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];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_j);
end
res(:,i,1) = res(:,i,1)+weights(k)*d1;
end
elseif j > 1 + (nnodes-1)*(i-2)
% new world, using previous state of world 1 and hit
% by shocks from nodes
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
k = j - (nnodes-1)*(i-2);
innovation(i+1,:) = nodes(k,:);
y = [Y(i_cols_p,1);
Y(i_cols_s,j);
Y(i_cols_f,j)];
[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = jacobian(:,i_cols_j);
res(:,i,j) = d1;
i_cols_Af = i_cols_Af + ny;
else
% existing worlds other than 1
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2+j-1);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
y = [Y(i_cols_p,j);
Y(i_cols_s,j);
Y(i_cols_f,j)];
[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = jacobian(:,i_cols_j);
res(:,i,j) = 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
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;
end
nzA = cell(periods,world_nbr);
parfor j=1:world_nbr
i_rows_y = find(lead_lag_incidence')+(order+1)*ny;
offset_c = ny*(order+(nnodes-1)*(order-1)*order/2+j-1);
offset_r = (j-1)*ny;
for i=order+2:periods
[d1,jacobian] = dynamic_model(Y(i_rows_y,j), ...
exo_simul,params, ...
steady_state,i+1);
if i == periods
[ir,ic,v] = find(jacobian(:,i_cols_T));
else
[ir,ic,v] = find(jacobian(:,i_cols_j));
end
nzA{i,j} = [offset_r+ir,offset_c+icA(ic), v]';
res(:,i,j) = d1;
i_rows_y = i_rows_y + ny;
offset_c = offset_c + world_nbr*ny;
offset_r = offset_r + world_nbr*ny;
end
end
err = max(abs(res(i_upd_r)));
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
A2 = [nzA{:}]';
A = [A1; sparse(A2(:,1),A2(:,2),A2(:,3),ny*(periods-order-1)*world_nbr,dimension)];
dy = -A\res(i_upd_r);
Y(i_upd_y) = Y(i_upd_y) + 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_.simul.maxit).']) ;
fprintf('\n') ;
end
flag = 1;% more iterations are needed.
endo_simul = 1;
end
if verbose
disp (['-----------------------------------------------------']) ;
end
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