237 lines
7.9 KiB
Matlab
237 lines
7.9 KiB
Matlab
function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model(endo_simul,exo_simul,pfm,nnodes,order)
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% Copyright © 2012-2017 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 <https://www.gnu.org/licenses/>.
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flag = 0;
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err = 0;
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stop = 0;
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params = pfm.params;
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steady_state = pfm.steady_state;
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ny = pfm.ny;
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periods = pfm.periods;
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dynamic_model = pfm.dynamic_model;
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lead_lag_incidence = pfm.lead_lag_incidence;
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lead_lag_incidence_t = transpose(lead_lag_incidence);
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nyp = pfm.nyp;
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nyf = pfm.nyf;
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i_cols_1 = pfm.i_cols_1;
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i_cols_j = pfm.i_cols_j;
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i_cols_T = nonzeros(lead_lag_incidence(1:2,:)');
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maxit = pfm.maxit_;
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tolerance = pfm.tolerance;
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verbose = pfm.verbose;
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number_of_shocks = size(exo_simul,2);
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[nodes,weights] = gauss_hermite_weights_and_nodes(nnodes);
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if number_of_shocks>1
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nodes = repmat(nodes,1,number_of_shocks)*chol(pfm.Sigma);
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% to be fixed for Sigma ~= I
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for i=number_of_shocks:-1:1
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rr(i) = {nodes(:,i)};
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ww(i) = {weights};
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end
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nodes = cartesian_product_of_sets(rr{:});
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weights = prod(cartesian_product_of_sets(ww{:}),2);
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nnodes = nnodes^number_of_shocks;
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else
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nodes = nodes*sqrt(pfm.Sigma);
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end
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if verbose
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disp (' -----------------------------------------------------');
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disp ('MODEL SIMULATION :');
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fprintf('\n');
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end
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z = endo_simul(lead_lag_incidence_t(:)>0);
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[~, jacobian] = dynamic_model(z, exo_simul, params,steady_state, 2);
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% Each column of Y represents a different world
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% The upper right cells are unused
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% The first row block is ny x 1
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% The second row block is ny x nnodes
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% The third row block is ny x nnodes^2
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% and so on until size ny x nnodes^order
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world_nbr = nnodes^order;
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Y = repmat(endo_simul(:),1,world_nbr);
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% The columns of A map the elements of Y such that
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% each block of Y with ny rows are unfolded column wise
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dimension = ny*(sum(nnodes.^(0:order-1),2)+(periods-order)*world_nbr);
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if order == 0
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i_upd_r = (1:ny*periods);
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i_upd_y = i_upd_r + ny;
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else
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i_upd_r = zeros(dimension,1);
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i_upd_y = i_upd_r;
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i_upd_r(1:ny) = (1:ny);
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i_upd_y(1:ny) = ny+(1:ny);
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i1 = ny+1;
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i2 = 2*ny;
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n1 = ny+1;
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n2 = 2*ny;
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for i=2:periods
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for j=1:nnodes^min(i-1,order)
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i_upd_r(i1:i2) = (n1:n2)+(j-1)*ny*periods;
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i_upd_y(i1:i2) = (n1:n2)+ny+(j-1)*ny*(periods+2);
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i1 = i2+1;
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i2 = i2+ny;
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end
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n1 = n2+1;
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n2 = n2+ny;
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end
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end
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if rows(lead_lag_incidence)>2
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icA = [find(lead_lag_incidence(1,:)) find(lead_lag_incidence(2,:))+world_nbr*ny ...
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find(lead_lag_incidence(3,:))+2*world_nbr*ny]';
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else
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if nyf
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icA = [find(lead_lag_incidence(2,:))+world_nbr*ny find(lead_lag_incidence(3,:))+2*world_nbr*ny ]';
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else
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icA = [find(lead_lag_incidence(1,:)) find(lead_lag_incidence(2,:))+world_nbr*ny ]';
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end
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end
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h1 = clock;
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for iter = 1:maxit
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A1 = sparse([],[],[],ny*(sum(nnodes.^(0:order-1),2)+1),dimension,(order+1)*world_nbr*nnz(jacobian));
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res = zeros(ny,periods,world_nbr);
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i_rows = 1:ny;
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i_cols = find(lead_lag_incidence');
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i_cols_p = i_cols(1:nyp);
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i_cols_s = i_cols(nyp+(1:ny));
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i_cols_f = i_cols(nyp+ny+(1:nyf));
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i_cols_Ap = i_cols_p;
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i_cols_As = i_cols_s;
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i_cols_Af = i_cols_f - ny;
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for i = 1:order+1
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i_w_p = 1;
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for j = 1:nnodes^(i-1)
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innovation = exo_simul;
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if i > 1
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innovation(i+1,:) = nodes(mod(j-1,nnodes)+1,:);
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end
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if i <= order
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for k=1:nnodes
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y = [Y(i_cols_p,i_w_p);
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Y(i_cols_s,j);
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Y(i_cols_f,(j-1)*nnodes+k)];
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[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
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if i == 1
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% in first period we don't keep track of
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% predetermined variables
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i_cols_A = [i_cols_As - ny; i_cols_Af];
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A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_1);
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else
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i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
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A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_j);
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end
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res(:,i,j) = res(:,i,j)+weights(k)*d1;
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i_cols_Af = i_cols_Af + ny;
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end
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else
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y = [Y(i_cols_p,i_w_p);
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Y(i_cols_s,j);
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Y(i_cols_f,j)];
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[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
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if i == 1
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% in first period we don't keep track of
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% predetermined variables
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i_cols_A = [i_cols_As - ny; i_cols_Af];
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A1(i_rows,i_cols_A) = jacobian(:,i_cols_1);
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else
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i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
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A1(i_rows,i_cols_A) = jacobian(:,i_cols_j);
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end
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res(:,i,j) = d1;
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i_cols_Af = i_cols_Af + ny;
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end
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i_rows = i_rows + ny;
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if mod(j,nnodes) == 0
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i_w_p = i_w_p + 1;
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end
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if i > 1
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if mod(j,nnodes) == 0
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i_cols_Ap = i_cols_Ap + ny;
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end
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i_cols_As = i_cols_As + ny;
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end
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end
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i_cols_p = i_cols_p + ny;
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i_cols_s = i_cols_s + ny;
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i_cols_f = i_cols_f + ny;
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end
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nzA = cell(periods,world_nbr);
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for j=1:world_nbr
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i_rows_y = find(lead_lag_incidence')+(order+1)*ny;
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offset_c = ny*(sum(nnodes.^(0:order-1),2)+j-1);
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offset_r = (j-1)*ny;
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for i=order+2:periods
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[d1,jacobian] = dynamic_model(Y(i_rows_y,j), ...
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exo_simul,params, ...
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steady_state,i+1);
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if i == periods
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[ir,ic,v] = find(jacobian(:,i_cols_T));
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else
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[ir,ic,v] = find(jacobian(:,i_cols_j));
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end
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nzA{i,j} = [offset_r+ir,offset_c+icA(ic), v]';
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res(:,i,j) = d1;
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i_rows_y = i_rows_y + ny;
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offset_c = offset_c + world_nbr*ny;
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offset_r = offset_r + world_nbr*ny;
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end
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end
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err = max(abs(res(i_upd_r)));
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if err < tolerance
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stop = 1;
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if verbose
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fprintf('\n') ;
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disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
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fprintf('\n') ;
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disp(' Convergency obtained.') ;
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fprintf('\n') ;
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end
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flag = 0;% Convergency obtained.
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endo_simul = reshape(Y(:,1),ny,periods+2);
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break
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end
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A2 = [nzA{:}]';
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A = [A1; sparse(A2(:,1),A2(:,2),A2(:,3),ny*(periods-order-1)*world_nbr,dimension)];
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dy = -A\res(i_upd_r);
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Y(i_upd_y) = Y(i_upd_y) + dy;
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end
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if ~stop
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if verbose
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fprintf('\n') ;
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disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
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fprintf('\n') ;
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disp('WARNING : maximum number of iterations is reached (modify options_.simul.maxit).') ;
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fprintf('\n') ;
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end
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flag = 1;% more iterations are needed.
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endo_simul = 1;
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end
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if verbose
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disp ('-----------------------------------------------------') ;
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end
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