103 lines
4.2 KiB
Matlab
103 lines
4.2 KiB
Matlab
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function [y, T, success, err, iter] = solve_two_boundaries_lbj(fh, y, x, steady_state, T, blk, options_, M_)
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% Computes the deterministic simulation of a block of equations containing
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% both lead and lag variables, using the LBJ algorithm.
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%
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% INPUTS
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% fh [handle] function handle to the dynamic file for the block
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% y [matrix] All the endogenous variables of the model
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% x [matrix] All the exogenous variables of the model
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% steady_state [vector] steady state of the model
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% T [matrix] Temporary terms
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% blk [integer] block number
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% options_ [structure] storing the options
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% M_ [structure] Model description
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%
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% OUTPUTS
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% y [matrix] All endogenous variables of the model
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% T [matrix] Temporary terms
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% success [logical] Whether a solution was found
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% err [double] ∞-norm of Δy
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% iter [integer] Number of iterations
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%
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% ALGORITHM
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% Laffargue, Boucekkine, Juillard (LBJ)
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% see Juillard (1996) Dynare: A program for the resolution and
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% simulation of dynamic models with forward variables through the use
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% of a relaxation algorithm. CEPREMAP. Couverture Orange. 9602.
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% Copyright © 2023 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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sparse_rowval = M_.block_structure.block(blk).g1_sparse_rowval;
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sparse_colval = M_.block_structure.block(blk).g1_sparse_colval;
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sparse_colptr = M_.block_structure.block(blk).g1_sparse_colptr;
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periods = options_.periods;
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% NB: notations are deliberately similar to those of sim1_lbj.m
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ny = M_.block_structure.block(blk).mfs;
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% Compute which columns, in the 3×n-wide Jacobian, have non-zero elements
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% corresponding to the forward (iyf) or backward (iyp) variables
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iyp = find(sparse_colptr(2:ny+1)-sparse_colptr(1:ny));
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iyf = find(sparse_colptr(2*ny+2:end)-sparse_colptr(2*ny+1:end-1));
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y_index = M_.block_structure.block(blk).variable(end-ny+1:end);
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success = false;
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for iter = 1:options_.simul.maxit
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h = clock;
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c = zeros(ny*periods, length(iyf)+1); % Stores the D and d of Sébastien’s presentation
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it_ = M_.maximum_lag+1;
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[yy, T(:, it_), r, g1] = fh(dynendo(y, it_, M_), x(it_, :), M_.params, steady_state, ...
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sparse_rowval, sparse_colval, sparse_colptr, T(:, it_));
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y(:, it_) = yy(M_.endo_nbr+(1:M_.endo_nbr));
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ic = 1:ny;
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icp = iyp;
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c(ic, :) = full(g1(:, ny+(1:ny))) \ [ full(g1(:, 2*ny+iyf)) -r ];
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for it_ = M_.maximum_lag+(2:periods)
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[yy, T(:, it_), r, g1] = fh(dynendo(y, it_, M_), x(it_, :), M_.params, steady_state, ...
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sparse_rowval, sparse_colval, sparse_colptr, T(:, it_));
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y(:, it_) = yy(M_.endo_nbr+(1:M_.endo_nbr));
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j = [ full(g1(:, ny+(1:ny))) -r ];
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j(:, [ iyf ny+1 ]) = j(:, [ iyf ny+1 ]) - full(g1(:, iyp)) * c(icp, :);
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ic = ic + ny;
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icp = icp + ny;
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c(ic, :) = j(:, 1:ny) \ [ full(g1(:, 2*ny+iyf)) j(:, ny+1) ];
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end
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dy = back_subst_lbj(c, ny, iyf, periods);
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y(y_index, M_.maximum_lag+(1:periods)) = y(y_index, M_.maximum_lag+(1:periods)) + dy;
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err = max(max(abs(dy)));
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if options_.verbosity
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fprintf('Iter: %s,\t err. = %s, \t time = %s\n', num2str(iter), num2str(err), num2str(etime(clock, h)));
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end
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if err < options_.dynatol.x
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success = true;
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break
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end
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end
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function y3n = dynendo(y, it_, M_)
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y3n = reshape(y(:, it_+(-1:1)), 3*M_.endo_nbr, 1);
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