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dynare/matlab/solve_two_boundaries.m

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Matlab
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function y = solve_two_boundaries(fname, y, x, params, y_index, nze, periods, y_kmin_l, y_kmax_l, is_linear, Block_Num, y_kmin, maxit_, solve_tolf, lambda, cutoff, simulation_method)
% Computes the deterministic simulation of a block of equation containing
% both lead and lag variables using relaxation methods
%
% INPUTS
% fname [string] name of the file containing the block
% to simulate
% 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
% 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
% y_kmin_l [integer] maximum number of lag in the block
% y_kmax_l [integer] maximum number of lead in the block
% is_linear [integer] if is_linear=1 the block is linear
% if is_linear=0 the block is not 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
% lambda [double] initial value of step size in
% Newton
% cutoff [double] cutoff to correct the direction in Newton in case
% of singular jacobian matrix
% simulation_method [integer] linear solver method used in the
% Newton algorithm :
% - 0 sprse LU
% - 2 GMRES
% - 3 BicGStab
%
% OUTPUTS
% y [matrix] All endogenous variables of the model
%
% ALGORITHM
% Newton with LU or GMRES or BicGstab
%
% SPECIAL REQUIREMENTS
% none.
%
% Copyright (C) 1996-2008 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/>.
global oo_;
cvg=0;
iter=0;
Per_u_=0;
g2 = [];
g3 = [];
Blck_size=size(y_index,2);
correcting_factor=0.01;
luinc_tol=1e-10;
max_resa=1e100;
Jacobian_Size=Blck_size*(y_kmin+y_kmax_l +periods);
g1=spalloc( Blck_size*periods, Jacobian_Size, nze*periods);
reduced = 0;
while ~(cvg==1 | iter>maxit_),
[r, g1, g2, g3, b]=feval(fname, y, x, params, periods, 0, y_kmin, Blck_size);
g1a=g1(:, y_kmin*Blck_size+1:(periods+y_kmin)*Blck_size);
%disp(['size(g1)=' int2str(size(g1))]);
%disp(['g1(:,' int2str(1:y_kmin_l*Blck_size) ')']);
%disp(['g1(:,' int2str((periods+y_kmin_l)*Blck_size+1:(periods+y_kmin_l+y_kmax_l)*Blck_size) ')']);
b = b' -g1(:, 1:y_kmin_l*Blck_size)*reshape(y(1+y_kmin-y_kmin_l:y_kmin,y_index)',1,y_kmin_l*Blck_size)'-g1(:, (periods+y_kmin_l)*Blck_size+1:(periods+y_kmin_l+y_kmax_l)*Blck_size)*reshape(y(periods+y_kmin+1:periods+y_kmin+y_kmax_l,y_index)',1,y_kmax_l*Blck_size)';
if(~isreal(r))
max_res=(-(max(max(abs(r))))^2)^0.5;
else
max_res=max(max(abs(r)));
end;
if(~isreal(max_res) | isnan(max_res))
cvg = 0;
elseif(is_linear & iter>0)
cvg = 1;
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(isnan(max_res))
detJ=det(g1aa);
if(abs(detJ)<1e-7)
max_factor=max(max(abs(g1aa)));
ze_elem=sum(diag(g1aa)<cutoff);
disp([num2str(full(ze_elem),'%d') ' elements on the Jacobian diagonal are below the cutoff (' num2str(cutoff,'%f') ')']);
if(correcting_factor<max_factor)
correcting_factor=correcting_factor*4;
disp(['The Jacobain 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')]);
dx = (g1aa+correcting_factor*speye(periods*Blck_size))\ba- ya;
y(1+y_kmin:periods+y_kmin,y_index)=reshape((ya_save+lambda*dx)',length(y_index),periods)';
continue;
else
disp('The singularity of the jacobian matrix could not be corrected');
return;
end;
end;
elseif(lambda>1e-8)
lambda=lambda/2;
reduced = 1;
disp(['reducing the path length: lambda=' num2str(lambda,'%f')]);
y(1+y_kmin:periods+y_kmin,y_index)=reshape((ya_save+lambda*dx)',length(y_index),periods)';
continue;
else
if(cutoff == 0)
fprintf('Error in simul: Convergence not achieved in block %d, after %d iterations.\n Increase "options_.maxit_".\n',Block_Num, iter);
else
fprintf('Error in simul: Convergence not achieved in block %d, after %d iterations.\n Increase "options_.maxit_" or set "cutoff=0" in model options.\n',Block_Num, iter);
end;
oo_.deterministic_simulation.status = 0;
oo_.deterministic_simulation.error = max_res;
oo_.deterministic_simulation.iterations = iter;
oo_.deterministic_simulation.block(Block_Num).status = 0;% Convergency failed.
oo_.deterministic_simulation.block(Block_Num).error = max_res;
oo_.deterministic_simulation.block(Block_Num).iterations = iter;
return;
end;
else
if(lambda<1)
lambda=max(lambda*2, 1);
end;
end;
end;
ya = reshape(y(y_kmin+1:y_kmin+periods,y_index)',1,periods*Blck_size)';
ya_save=ya;
g1aa=g1a;
ba=b;
max_resa=max_res;
if(simulation_method==0),
dx = g1a\b- ya;
ya = ya + lambda*dx;
y(1+y_kmin:periods+y_kmin,y_index)=reshape(ya',length(y_index),periods)';
elseif(simulation_method==2),
flag1=1;
while(flag1>0)
[L1, U1]=luinc(g1a,luinc_tol);
[za,flag1] = gmres(g1a,b,Blck_size,1e-6,Blck_size*periods,L1,U1);
if (flag1>0 | reduced)
if(flag1==1)
disp(['Error in simul: No convergence inside GMRES after ' num2str(periods*10,'%6d') ' iterations, in block' num2str(Block_Size,'%3d')]);
elseif(flag1==2)
disp(['Error in simul: Preconditioner is ill-conditioned, in block' num2str(Block_Size,'%3d')]);
elseif(flag1==3)
disp(['Error in simul: GMRES stagnated (Two consecutive iterates were the same.), in block' num2str(Block_Size,'%3d')]);
end;
luinc_tol = luinc_tol/10;
reduced = 0;
else
dx = za - ya;
ya = ya + lambda*dx;
y(1+y_kmin:periods+y_kmin,y_index)=reshape(ya',length(y_index),periods)';
end;
end;
elseif(simulation_method==3),
flag1=1;
while(flag1>0)
[L1, U1]=luinc(g1a,luinc_tol);
[za,flag1] = bicgstab(g1a,b,1e-7,Blck_size*periods,L1,U1);
if (flag1>0 | reduced)
if(flag1==1)
disp(['Error in simul: No convergence inside BICGSTAB after ' num2str(periods*10,'%6d') ' iterations, in block' num2str(Block_Size,'%3d')]);
elseif(flag1==2)
disp(['Error in simul: Preconditioner is ill-conditioned, in block' num2str(Block_Size,'%3d')]);
elseif(flag1==3)
disp(['Error in simul: GMRES stagnated (Two consecutive iterates were the same.), in block' num2str(Block_Size,'%3d')]);
end;
luinc_tol = luinc_tol/10;
reduced = 0;
else
dx = za - ya;
ya = ya + lambda*dx;
y(1+y_kmin:periods+y_kmin,y_index)=reshape(ya',length(y_index),periods)';
end;
end;
end;
end
iter=iter+1;
disp(['iteration: ' num2str(iter,'%d') ' error: ' num2str(max_res,'%e')]);
end;
if (iter>maxit_)
disp(['No convergence after ' num2str(iter,'%4d') ' iterations in Block ' num2str(Block_Num,'%d')]);
oo_.deterministic_simulation.status = 0;
oo_.deterministic_simulation.error = max_res;
oo_.deterministic_simulation.iterations = iter;
oo_.deterministic_simulation.block(Block_Num).status = 0;% Convergency failed.
oo_.deterministic_simulation.block(Block_Num).error = max_res;
oo_.deterministic_simulation.block(Block_Num).iterations = iter;
return;
end
oo_.deterministic_simulation.status = 1;
oo_.deterministic_simulation.error = max_res;
oo_.deterministic_simulation.iterations = iter;
oo_.deterministic_simulation.block(Block_Num).status = 1;% Convergency obtained.
oo_.deterministic_simulation.block(Block_Num).error = max_res;
oo_.deterministic_simulation.block(Block_Num).iterations = iter;
return;
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