340 lines
16 KiB
Matlab
340 lines
16 KiB
Matlab
function [y, oo]= solve_two_boundaries(fname, y, x, params, steady_state, y_index, nze, periods, y_kmin_l, y_kmax_l, is_linear, Block_Num, y_kmin, maxit_, solve_tolf, lambda, cutoff, stack_solve_algo,options,M, oo)
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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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% steady_state [vector] steady state 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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% stack_solve_algo [integer] linear solver method used in the
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% Newton algorithm :
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% - 1 sprse LU
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% - 2 GMRES
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% - 3 BicGStab
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% - 4 Optimal path length
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% M [structure] Model description
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% oo [structure] Results
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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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% oo [structure] Results
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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) 1996-2018 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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verbose = options.verbosity;
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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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ilu_setup.droptol=1e-10;
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ilu_setup.type = 'ilutp';
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%ilu_setup.milu = 'col';
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ilu_setup.milu = 'off';
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ilu_setup.thresh = 1;
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ilu_setup.udiag = 0;
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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, y, g1, g2, g3, b]=feval(fname, y, x, params, steady_state, periods, 0, y_kmin, Blck_size,options.periods);
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preconditioner = 2;
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g1a=g1(:, y_kmin*Blck_size+1:(periods+y_kmin)*Blck_size);
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term1 = 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)';
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term2 = 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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b = b - term1 - term2;
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[max_res, max_indx]=max(max(abs(r')));
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if ~isreal(r)
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max_res = (-max_res^2)^0.5;
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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 verbose && ~isreal(max_res)
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disp(['Variable ' M.endo_names{max_indx} ' (' int2str(max_indx) ') returns an undefined value']);
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end
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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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if verbose
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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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end
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if correcting_factor<max_factor
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correcting_factor=correcting_factor*4;
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if verbose
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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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end
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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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if verbose
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disp(['reducing the path length: lambda=' num2str(lambda,'%f')]);
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end
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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 verbose
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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_.simul.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_.simul.maxit" or set "cutoff=0" in model options.\n',Block_Num, iter);
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end
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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 stack_solve_algo==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 stack_solve_algo==1
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for t=1:periods
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first_elem = (t-1)*Blck_size+1;
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last_elem = t*Blck_size;
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next_elem = (t+1)*Blck_size;
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Elem = first_elem:last_elem;
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Elem_1 = last_elem+1:next_elem;
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B1_inv = inv(g1a(Elem, Elem));
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if (t < periods)
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S1 = B1_inv * g1a(Elem, Elem_1);
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end
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g1a(Elem, Elem_1) = S1;
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b(Elem) = B1_inv * b(Elem);
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g1a(Elem, Elem) = ones(Blck_size, Blck_size);
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if t<periods
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g1a(Elem_1, Elem_1) = g1a(Elem_1, Elem_1) - g1a(Elem_1, Elem) * S1;
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b(Elem_1) = b(Elem_1) - g1a(Elem_1, Elem) * b(Elem);
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g1a(Elem_1, Elem) = zeros(Blck_size, Blck_size);
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end
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end
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za = b(Elem);
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zaa = za;
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y_Elem = (periods - 1) * Blck_size + 1:(periods) * Blck_size;
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dx = ya;
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dx(y_Elem) = za - ya(y_Elem);
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ya(y_Elem) = ya(y_Elem) + lambda*dx(y_Elem);
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for t=periods-1:-1:1
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first_elem = (t-1)*Blck_size+1;
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last_elem = t*Blck_size;
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next_elem = (t+1)*Blck_size;
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Elem_1 = last_elem+1:next_elem;
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Elem = first_elem:last_elem;
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za = b(Elem) - g1a(Elem, Elem_1) * zaa;
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zaa = za;
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y_Elem = Blck_size * (t-1)+1:Blck_size * (t);
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dx(y_Elem) = za - ya(y_Elem);
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ya(y_Elem) = ya(y_Elem) + lambda*dx(y_Elem);
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y(y_kmin + t, y_index) = ya(y_Elem);
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end
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elseif stack_solve_algo==2
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flag1=1;
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while flag1>0
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if preconditioner==2
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[L1, U1]=ilu(g1a,ilu_setup);
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elseif preconditioner==3
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Size = Blck_size;
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gss1 = g1a(Size + 1: 2*Size,Size + 1: 2*Size) + g1a(Size + 1: 2*Size,2*Size+1: 3*Size);
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[L1, U1]=lu(gss1);
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L(1:Size,1:Size) = L1;
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U(1:Size,1:Size) = U1;
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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);
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[L2, U2]=lu(gss2);
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L(Size+1:(periods-1)*Size,Size+1:(periods-1)*Size) = kron(eye(periods-2), L2);
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U(Size+1:(periods-1)*Size,Size+1:(periods-1)*Size) = kron(eye(periods-2), U2);
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gss2 = g1a(Size + 1: 2*Size,1: Size) + g1a(Size + 1: 2*Size,Size+1: 2*Size);
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[L3, U3]=lu(gss2);
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L((periods-1)*Size+1:periods*Size,(periods-1)*Size+1:periods*Size) = L3;
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U((periods-1)*Size+1:periods*Size,(periods-1)*Size+1:periods*Size) = U3;
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L1 = L;
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U1 = U;
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elseif preconditioner==4
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Size = Blck_size;
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gss1 = g1a(1: 3*Size, 1: 3*Size);
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[L, U] = lu(gss1);
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L1 = kron(eye(ceil(periods/3)),L);
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U1 = kron(eye(ceil(periods/3)),U);
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L1 = L1(1:periods * Size, 1:periods * Size);
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U1 = U1(1:periods * Size, 1:periods * Size);
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end
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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 verbose
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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(Blck_size,'%3d')]);
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elseif flag1==2
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disp(['Error in simul: Preconditioner is ill-conditioned, in block ' num2str(Blck_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(Blck_size,'%3d')]);
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end
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end
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ilu_setup.droptol = ilu_setup.droptol/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 stack_solve_algo==3
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flag1=1;
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while flag1>0
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if preconditioner==2
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[L1, U1]=ilu(g1a,ilu_setup);
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[za,flag1] = bicgstab(g1a,b,1e-7,Blck_size*periods,L1,U1);
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elseif preconditioner==3
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Size = Blck_size;
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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);
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[L1, U1]=lu(gss0);
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P1 = eye(size(gss0));
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Q1 = eye(size(gss0));
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L = kron(eye(periods),L1);
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U = kron(eye(periods),U1);
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P = kron(eye(periods),P1);
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Q = kron(eye(periods),Q1);
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[za,flag1] = bicgstab1(g1a,b,1e-7,Blck_size*periods,L,U, P, Q);
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else
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Size = Blck_size;
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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);
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[L1, U1]=lu(gss0);
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L1 = kron(eye(periods),L1);
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U1 = kron(eye(periods),U1);
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[za,flag1] = bicgstab(g1a,b,1e-7,Blck_size*periods,L1,U1);
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end
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if flag1>0 || reduced
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if verbose
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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(Blck_size,'%3d')]);
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elseif flag1==2
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disp(['Error in simul: Preconditioner is ill-conditioned, in block ' num2str(Blck_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(Blck_size,'%3d')]);
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end
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end
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ilu_setup.droptol = ilu_setup.droptol/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 stack_solve_algo==4
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ra = reshape(r(:, y_kmin+1:periods+y_kmin),periods*Blck_size, 1);
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stpmx = 100 ;
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stpmax = stpmx*max([sqrt(ya'*ya);size(y_index,2)]);
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nn=1:size(ra,1);
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g = (ra'*g1a)';
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f = 0.5*ra'*ra;
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p = -g1a\ra;
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[yn,f,ra,check]=lnsrch1(ya,f,g,p,stpmax,'lnsrch1_wrapper_two_boundaries',nn,nn, options.solve_tolx, fname, y, y_index,x, params, steady_state, periods, y_kmin, Blck_size,options.periods);
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dx = ya - yn;
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y(1+y_kmin:periods+y_kmin,y_index)=reshape(yn',length(y_index),periods)';
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end
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end
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iter=iter+1;
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if verbose
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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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if verbose
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printline(41)
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%disp(['No convergence after ' num2str(iter,'%4d') ' iterations in Block ' num2str(Block_Num,'%d')])
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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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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; |