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Much faster .m implementation of LBJ with block option

kalman_mex
Sébastien Villemot 2023-11-08 16:55:37 +01:00
parent 0839ff78ae
commit be648d350b
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GPG Key ID: 2CECE9350ECEBE4A
5 changed files with 159 additions and 70 deletions
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43
matlab/perfect-foresight-models/back_subst_lbj.m Normal file
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@ -0,0 +1,43 @@
function dy = back_subst_lbj(c,ny,iyf,periods)
% Computes backward substitution in LBJ
%
% INPUTS
% c: matrix containing the D and d for Sébastien’s presentation
% ny: number of endogenous variables
% iyf: indices of forward variables inside the list of all endogenous variables
% periods: number of simulation periods
%
% OUTPUTS
% dy: vector of backsubstitution results
% Copyright © 2023 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 <https://www.gnu.org/licenses/>.
ir = (periods-2)*ny+(1:ny);
irf = iyf+(periods-1)*ny;
icf = 1:size(iyf,2);
nrc = length(iyf)+1;
for i = 2:periods
c(ir,nrc) = c(ir,nrc)-c(ir,icf)*c(irf,nrc);
ir = ir-ny;
irf = irf-ny;
end
dy = reshape(c(:,nrc), ny, periods);
end

27
matlab/perfect-foresight-models/sim1_lbj.m
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@ -94,8 +94,7 @@ for iter = 1:options_.simul.maxit
icp = icp + ny;
c (ic,:) = jacobian(:,is)\jacobian(:,isf1);
end
c = bksup1(c, ny, nrc, iyf, options_.periods);
c = reshape(c, ny, options_.periods);
c = back_subst_lbj(c, ny, iyf, options_.periods);
endogenousvariables(:,M_.maximum_lag+(1:options_.periods)) = endogenousvariables(:,M_.maximum_lag+(1:options_.periods))+c;
err = max(max(abs(c)));
if verbose
@ -119,27 +118,3 @@ if verbose
end
end
function d = bksup1(c,ny,jcf,iyf,periods)
% Solves deterministic models recursively by backsubstitution for one lead/lag
%
% INPUTS
% ny: number of endogenous variables
% jcf: variables index forward
%
% OUTPUTS
% d: vector of backsubstitution results
ir = [(periods-2)*ny+1:ny+(periods-2)*ny];
irf = iyf+(periods-1)*ny;
icf = [1:size(iyf,2)];
for i = 2:periods
c(ir,jcf) = c(ir,jcf)-c(ir,icf)*c(irf,jcf);
ir = ir-ny;
irf = irf-ny;
end
d = c(:,jcf);
end

6
matlab/perfect-foresight-models/solve_block_decomposed_problem.m
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@ -92,7 +92,11 @@ for blk = 1:nblocks
y_index = M_.block_structure.block(blk).variable(end-M_.block_structure.block(blk).mfs+1:end);
[y, T, success, maxblkerror, iter] = solve_one_boundary(fh_dynamic, y, exo_simul, M_.params, steady_state, T, y_index, M_.block_structure.block(blk).NNZDerivatives, options_.periods, M_.block_structure.block(blk).is_linear, blk, M_.maximum_lag, options_.simul.maxit, options_.dynatol.f, cutoff, options_.stack_solve_algo, is_forward, true, false, M_, options_);
case {5, 8} % solveTwoBoundaries{Simple,Complete}
[y, T, success, maxblkerror, iter] = solve_two_boundaries(fh_dynamic, y, exo_simul, steady_state, T, blk, cutoff, options_, M_);
if ismember(options_.stack_solve_algo, [1 6])
[y, T, success, maxblkerror, iter] = solve_two_boundaries_lbj(fh_dynamic, y, exo_simul, steady_state, T, blk, options_, M_);
else
[y, T, success, maxblkerror, iter] = solve_two_boundaries_stacked(fh_dynamic, y, exo_simul, steady_state, T, blk, cutoff, options_, M_);
end
end
tmp = y(M_.block_structure.block(blk).variable, :);

102
matlab/perfect-foresight-models/solve_two_boundaries_lbj.m Normal file
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@ -0,0 +1,102 @@
function [y, T, success, err, iter] = solve_two_boundaries_lbj(fh, y, x, steady_state, T, blk, options_, M_)
% Computes the deterministic simulation of a block of equations containing
% both lead and lag variables, using the LBJ algorithm.
%
% INPUTS
% fh [handle] function handle to the dynamic file for the block
% y [matrix] All the endogenous variables of the model
% x [matrix] All the exogenous variables of the model
% steady_state [vector] steady state of the model
% T [matrix] Temporary terms
% blk [integer] block number
% options_ [structure] storing the options
% M_ [structure] Model description
%
% OUTPUTS
% y [matrix] All endogenous variables of the model
% T [matrix] Temporary terms
% success [logical] Whether a solution was found
% err [double] ∞-norm of Δy
% iter [integer] Number of iterations
%
% ALGORITHM
% Laffargue, Boucekkine, Juillard (LBJ)
% see Juillard (1996) Dynare: A program for the resolution and
% simulation of dynamic models with forward variables through the use
% of a relaxation algorithm. CEPREMAP. Couverture Orange. 9602.
% Copyright © 2023 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 <https://www.gnu.org/licenses/>.
sparse_rowval = M_.block_structure.block(blk).g1_sparse_rowval;
sparse_colval = M_.block_structure.block(blk).g1_sparse_colval;
sparse_colptr = M_.block_structure.block(blk).g1_sparse_colptr;
periods = options_.periods;
% NB: notations are deliberately similar to those of sim1_lbj.m
ny = M_.block_structure.block(blk).mfs;
% Compute which columns, in the 3×n-wide Jacobian, have non-zero elements
% corresponding to the forward (iyf) or backward (iyp) variables
iyp = find(sparse_colptr(2:ny+1)-sparse_colptr(1:ny));
iyf = find(sparse_colptr(2*ny+2:end)-sparse_colptr(2*ny+1:end-1));
y_index = M_.block_structure.block(blk).variable(end-ny+1:end);
success = false;
for iter = 1:options_.simul.maxit
h = clock;
c = zeros(ny*periods, length(iyf)+1); % Stores the D and d of Sébastien’s presentation
it_ = M_.maximum_lag+1;
[yy, T(:, it_), r, g1] = fh(dynendo(y, it_, M_), x(it_, :), M_.params, steady_state, ...
sparse_rowval, sparse_colval, sparse_colptr, T(:, it_));
y(:, it_) = yy(M_.endo_nbr+(1:M_.endo_nbr));
ic = 1:ny;
icp = iyp;
c(ic, :) = full(g1(:, ny+(1:ny))) \ [ full(g1(:, 2*ny+iyf)) -r ];
for it_ = M_.maximum_lag+(2:periods)
[yy, T(:, it_), r, g1] = fh(dynendo(y, it_, M_), x(it_, :), M_.params, steady_state, ...
sparse_rowval, sparse_colval, sparse_colptr, T(:, it_));
y(:, it_) = yy(M_.endo_nbr+(1:M_.endo_nbr));
j = [ full(g1(:, ny+(1:ny))) -r ];
j(:, [ iyf ny+1 ]) = j(:, [ iyf ny+1 ]) - full(g1(:, iyp)) * c(icp, :);
ic = ic + ny;
icp = icp + ny;
c(ic, :) = j(:, 1:ny) \ [ full(g1(:, 2*ny+iyf)) j(:, ny+1) ];
end
dy = back_subst_lbj(c, ny, iyf, periods);
y(y_index, M_.maximum_lag+(1:periods)) = y(y_index, M_.maximum_lag+(1:periods)) + dy;
err = max(max(abs(dy)));
if options_.verbosity
fprintf('Iter: %s,\t err. = %s, \t time = %s\n', num2str(iter), num2str(err), num2str(etime(clock, h)));
end
if err < options_.dynatol.x
success = true;
break
end
end
function y3n = dynendo(y, it_, M_)
y3n = reshape(y(:, it_+(-1:1)), 3*M_.endo_nbr, 1);

51
matlab/solve_two_boundaries.m → matlab/perfect-foresight-models/solve_two_boundaries_stacked.m
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@ -1,6 +1,7 @@
function [y, T, success, max_res, iter] = solve_two_boundaries(fh, y, x, steady_state, T, Block_Num, cutoff, options_, M_)
% Computes the deterministic simulation of a block of equation containing
% both lead and lag variables using relaxation methods
function [y, T, success, max_res, iter] = solve_two_boundaries_stacked(fh, y, x, steady_state, T, Block_Num, cutoff, options_, M_)
% Computes the deterministic simulation of a block of equations containing
% both lead and lag variables, using a Newton method over the stacked Jacobian
% (in particular, this excludes LBJ).
%
% INPUTS
% fh [handle] function handle to the dynamic file for the block
@ -47,6 +48,10 @@ periods = options_.periods;
y_kmin = M_.maximum_lag;
stack_solve_algo = options_.stack_solve_algo;
if ~ismember(stack_solve_algo, [0 2 3 4])
error('Unsupported stack_solve_algo value')
end
verbose = options_.verbosity;
cvg=false;
@ -158,46 +163,6 @@ while ~(cvg || iter > options_.simul.maxit)
dx = g1a\b- ya;
ya = ya + lambda*dx;
y(y_index, y_kmin+(1:periods))=reshape(ya',length(y_index),periods);
elseif stack_solve_algo==1 || stack_solve_algo==6
for t=1:periods
first_elem = (t-1)*Blck_size+1;
last_elem = t*Blck_size;
next_elem = (t+1)*Blck_size;
Elem = first_elem:last_elem;
Elem_1 = last_elem+1:next_elem;
B1_inv = inv(g1a(Elem, Elem));
if (t < periods)
S1 = B1_inv * g1a(Elem, Elem_1);
g1a(Elem, Elem_1) = S1;
end
b(Elem) = B1_inv * b(Elem);
g1a(Elem, Elem) = ones(Blck_size, Blck_size);
if t<periods
g1a(Elem_1, Elem_1) = g1a(Elem_1, Elem_1) - g1a(Elem_1, Elem) * S1;
b(Elem_1) = b(Elem_1) - g1a(Elem_1, Elem) * b(Elem);
g1a(Elem_1, Elem) = zeros(Blck_size, Blck_size);
end
end
za = b(Elem);
zaa = za;
y_Elem = (periods - 1) * Blck_size + 1:(periods) * Blck_size;
dx = ya;
dx(y_Elem) = za - ya(y_Elem);
ya(y_Elem) = ya(y_Elem) + lambda*dx(y_Elem);
y(y_index, y_kmin + periods) = ya(y_Elem);
for t=periods-1:-1:1
first_elem = (t-1)*Blck_size+1;
last_elem = t*Blck_size;
next_elem = (t+1)*Blck_size;
Elem_1 = last_elem+1:next_elem;
Elem = first_elem:last_elem;
za = b(Elem) - g1a(Elem, Elem_1) * zaa;
zaa = za;
y_Elem = Blck_size * (t-1)+1:Blck_size * (t);
dx(y_Elem) = za - ya(y_Elem);
ya(y_Elem) = ya(y_Elem) + lambda*dx(y_Elem);
y(y_index, y_kmin + t) = ya(y_Elem);
end
elseif stack_solve_algo==2
flag1=1;
while flag1>0