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