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dynare/matlab/solve_two_boundaries.m

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Matlab
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function [y, T, success, max_res, iter] = solve_two_boundaries(fh, y, x, params, steady_state, T, y_index, nze, periods, is_linear, Block_Num, y_kmin, maxit_, solve_tolf, cutoff, stack_solve_algo,options_,M_)
% Computes the deterministic simulation of a block of equation containing
% both lead and lag variables using relaxation methods
%
% 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
% params [vector] All the parameters of the model
% steady_state [vector] steady state of the model
% T [matrix] Temporary terms
% y_index [vector of int] The index of the endogenous variables of
% the block
% nze [integer] number of non-zero elements in the
% jacobian matrix
% periods [integer] number of simulation periods
% is_linear [logical] Whether the block is linear
% Block_Num [integer] block number
% y_kmin [integer] maximum number of lag in the model
% maxit_ [integer] maximum number of iteration in Newton
% solve_tolf [double] convergence criteria
% cutoff [double] cutoff to correct the direction in Newton in case
% of singular jacobian matrix
% stack_solve_algo [integer] linear solver method used in the
% Newton algorithm :
% - 1 sprse LU
% - 2 GMRES
% - 3 BicGStab
% - 4 Optimal path length
% 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
% max_res [double] ∞-norm of the residual
% iter [integer] Number of iterations
%
% ALGORITHM
% Newton with LU or GMRES or BicGstab
% Copyright © 1996-2023 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/>.
verbose = options_.verbosity;
cvg=false;
iter=0;
Per_u_=0;
Blck_size=size(y_index,2);
correcting_factor=0.01;
ilu_setup.droptol=1e-10;
ilu_setup.type = 'ilutp';
%ilu_setup.milu = 'col';
ilu_setup.milu = 'off';
ilu_setup.thresh = 1;
ilu_setup.udiag = 0;
max_resa=1e100;
lambda = 1; % Length of Newton step
reduced = 0;
while ~(cvg || iter>maxit_)
r = NaN(Blck_size, periods);
g1a = spalloc(Blck_size*periods, Blck_size*periods, nze*periods);
for it_ = y_kmin+(1:periods)
[yy, T(:, it_), r(:, it_-y_kmin), g1]=fh(dynendo(y, it_, M_), x(it_, :), params, steady_state, ...
M_.block_structure.block(Block_Num).g1_sparse_rowval, ...
M_.block_structure.block(Block_Num).g1_sparse_colval, ...
M_.block_structure.block(Block_Num).g1_sparse_colptr, T(:, it_));
y(:, it_) = yy(M_.endo_nbr+(1:M_.endo_nbr));
if periods == 1
g1a = g1(:, Blck_size+(1:Blck_size));
elseif it_ == y_kmin+1
g1a(1:Blck_size, 1:Blck_size*2) = g1(:, Blck_size+1:end);
elseif it_ == y_kmin+periods
g1a((periods-1)*Blck_size+1:end, (periods-2)*Blck_size+1:end) = g1(:, 1:2*Blck_size);
else
g1a((it_-y_kmin-1)*Blck_size+(1:Blck_size), (it_-y_kmin-2)*Blck_size+(1:3*Blck_size)) = g1;
end
end
preconditioner = 2;
ya = reshape(y(y_index, y_kmin+(1:periods)), 1, periods*Blck_size)';
ra = reshape(r, periods*Blck_size, 1);
b=-ra+g1a*ya;
[max_res, max_indx]=max(max(abs(r')));
if ~isreal(r)
max_res = (-max_res^2)^0.5;
end
if ~isreal(max_res) || isnan(max_res)
cvg = false;
elseif is_linear && iter>0
cvg = true;
else
cvg=(max_res<solve_tolf);
end
if ~cvg
if iter>0
if ~isreal(max_res) || isnan(max_res) || (max_resa<max_res && iter>1)
if verbose && ~isreal(max_res)
disp(['Variable ' M_.endo_names{max_indx} ' (' int2str(max_indx) ') returns an undefined value']);
end
if isnan(max_res)
detJ=det(g1aa);
if abs(detJ)<1e-7
max_factor=max(max(abs(g1aa)));
ze_elem=sum(diag(g1aa)<cutoff);
if verbose
disp([num2str(full(ze_elem),'%d') ' elements on the Jacobian diagonal are below the cutoff (' num2str(cutoff,'%f') ')']);
end
if correcting_factor<max_factor
correcting_factor=correcting_factor*4;
if verbose
disp(['The Jacobian matrix is singular, det(Jacobian)=' num2str(detJ,'%f') '.']);
disp([' trying to correct the Jacobian matrix:']);
disp([' correcting_factor=' num2str(correcting_factor,'%f') ' max(Jacobian)=' num2str(full(max_factor),'%f')]);
end
dx = (g1aa+correcting_factor*speye(periods*Blck_size))\ba- ya_save;
y(y_index, y_kmin+(1:periods))=reshape((ya_save+lambda*dx)',length(y_index),periods);
continue
else
disp('The singularity of the jacobian matrix could not be corrected');
success = false;
return
end
end
elseif lambda>1e-8
lambda=lambda/2;
reduced = 1;
if verbose
disp(['reducing the path length: lambda=' num2str(lambda,'%f')]);
end
y(y_index, y_kmin+(1:periods))=reshape((ya_save+lambda*dx)',length(y_index),periods);
continue
else
if verbose
if cutoff==0
fprintf('Convergence not achieved in block %d, after %d iterations.\n Increase "maxit".\n',Block_Num, iter);
else
fprintf('Convergence not achieved in block %d, after %d iterations.\n Increase "maxit" or set "cutoff=0" in model options.\n',Block_Num, iter);
end
end
success = false;
return
end
else
if lambda<1
lambda=max(lambda*2, 1);
end
end
end
ya_save=ya;
g1aa=g1a;
ba=b;
max_resa=max_res;
if stack_solve_algo==0
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
if preconditioner==2
[L1, U1]=ilu(g1a,ilu_setup);
elseif preconditioner==3
Size = Blck_size;
gss1 = g1a(Size + 1: 2*Size,Size + 1: 2*Size) + g1a(Size + 1: 2*Size,2*Size+1: 3*Size);
[L1, U1]=lu(gss1);
L(1:Size,1:Size) = L1;
U(1:Size,1:Size) = U1;
gss2 = g1a(Size + 1: 2*Size,1: Size) + g1a(Size + 1: 2*Size,Size+1: 2*Size) + g1a(Size + 1: 2*Size,2*Size+1: 3*Size);
[L2, U2]=lu(gss2);
L(Size+1:(periods-1)*Size,Size+1:(periods-1)*Size) = kron(eye(periods-2), L2);
U(Size+1:(periods-1)*Size,Size+1:(periods-1)*Size) = kron(eye(periods-2), U2);
gss2 = g1a(Size + 1: 2*Size,1: Size) + g1a(Size + 1: 2*Size,Size+1: 2*Size);
[L3, U3]=lu(gss2);
L((periods-1)*Size+1:periods*Size,(periods-1)*Size+1:periods*Size) = L3;
U((periods-1)*Size+1:periods*Size,(periods-1)*Size+1:periods*Size) = U3;
L1 = L;
U1 = U;
elseif preconditioner==4
Size = Blck_size;
gss1 = g1a(1: 3*Size, 1: 3*Size);
[L, U] = lu(gss1);
L1 = kron(eye(ceil(periods/3)),L);
U1 = kron(eye(ceil(periods/3)),U);
L1 = L1(1:periods * Size, 1:periods * Size);
U1 = U1(1:periods * Size, 1:periods * Size);
end
[za,flag1] = gmres(g1a,b,Blck_size,1e-6,Blck_size*periods,L1,U1);
if (flag1>0 || reduced)
if verbose
if flag1==1
disp(['Error in simul: No convergence inside GMRES after ' num2str(periods*10,'%6d') ' iterations, in block ' num2str(Blck_size,'%3d')]);
elseif flag1==2
disp(['Error in simul: Preconditioner is ill-conditioned, in block ' num2str(Blck_size,'%3d')]);
elseif flag1==3
disp(['Error in simul: GMRES stagnated (Two consecutive iterates were the same.), in block ' num2str(Blck_size,'%3d')]);
end
end
ilu_setup.droptol = ilu_setup.droptol/10;
reduced = 0;
else
dx = za - ya;
ya = ya + lambda*dx;
y(y_index, y_kmin+(1:periods))=reshape(ya',length(y_index),periods);
end
end
elseif stack_solve_algo==3
flag1=1;
while flag1>0
if preconditioner==2
[L1, U1]=ilu(g1a,ilu_setup);
[za,flag1] = bicgstab(g1a,b,1e-7,Blck_size*periods,L1,U1);
elseif preconditioner==3
Size = Blck_size;
gss0 = g1a(Size + 1: 2*Size,1: Size) + g1a(Size + 1: 2*Size,Size+1: 2*Size) + g1a(Size + 1: 2*Size,2*Size+1: 3*Size);
[L1, U1]=lu(gss0);
P1 = eye(size(gss0));
Q1 = eye(size(gss0));
L = kron(eye(periods),L1);
U = kron(eye(periods),U1);
P = kron(eye(periods),P1);
Q = kron(eye(periods),Q1);
[za,flag1] = bicgstab1(g1a,b,1e-7,Blck_size*periods,L,U, P, Q);
else
Size = Blck_size;
gss0 = g1a(Size + 1: 2*Size,1: Size) + g1a(Size + 1: 2*Size,Size+1: 2*Size) + g1a(Size + 1: 2*Size,2*Size+1: 3*Size);
[L1, U1]=lu(gss0);
L1 = kron(eye(periods),L1);
U1 = kron(eye(periods),U1);
[za,flag1] = bicgstab(g1a,b,1e-7,Blck_size*periods,L1,U1);
end
if flag1>0 || reduced
if verbose
if flag1==1
disp(['Error in simul: No convergence inside BICGSTAB after ' num2str(periods*10,'%6d') ' iterations, in block ' num2str(Blck_size,'%3d')]);
elseif flag1==2
disp(['Error in simul: Preconditioner is ill-conditioned, in block ' num2str(Blck_size,'%3d')]);
elseif flag1==3
disp(['Error in simul: GMRES stagnated (Two consecutive iterates were the same.), in block ' num2str(Blck_size,'%3d')]);
end
end
ilu_setup.droptol = ilu_setup.droptol/10;
reduced = 0;
else
dx = za - ya;
ya = ya + lambda*dx;
y(y_index, y_kmin+(1:periods))=reshape(ya',length(y_index),periods);
end
end
elseif stack_solve_algo==4
stpmx = 100 ;
stpmax = stpmx*max([sqrt(ya'*ya);size(y_index,2)]);
nn=1:size(ra,1);
g = (ra'*g1a)';
f = 0.5*ra'*ra;
p = -g1a\ra;
[yn,f,ra,check]=lnsrch1(ya,f,g,p,stpmax,@lnsrch1_wrapper_two_boundaries,nn,nn, options_.solve_tolx, fh, Block_Num, y, y_index,x, params, steady_state, T, periods, Blck_size, M_);
dx = ya - yn;
y(y_index, y_kmin+(1:periods))=reshape(yn',length(y_index),periods);
end
end
iter=iter+1;
if verbose
disp(['iteration: ' num2str(iter,'%d') ' error: ' num2str(max_res,'%e')]);
end
end
if (iter>maxit_)
if verbose
printline(41)
%disp(['No convergence after ' num2str(iter,'%4d') ' iterations in Block ' num2str(Block_Num,'%d')])
end
success = false;
return
end
success = true;
function y3n = dynendo(y, it_, M_)
y3n = reshape(y(:, it_+(-1:1)), 3*M_.endo_nbr, 1);
function ra = lnsrch1_wrapper_two_boundaries(ya, fh, Block_Num, y, y_index, x, ...
params, steady_state, T, periods, ...
y_size, M_)
y(y_index, M_.maximum_lag+(1:periods)) = reshape(ya',length(y_index),periods);
ra = NaN(periods*y_size, 1);
for it_ = M_.maximum_lag+(1:periods)
[~, ~, ra((it_-M_.maximum_lag-1)*y_size+(1:y_size)), g1] = fh(dynendo(y, it_, M_), x(it_, :), params, steady_state, M_.block_structure.block(Block_Num).g1_sparse_rowval, M_.block_structure.block(Block_Num).g1_sparse_colval, M_.block_structure.block(Block_Num).g1_sparse_colptr, T(:, it_));
end
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