369 lines
18 KiB
Matlab
369 lines
18 KiB
Matlab
function [ide_hess, ide_moments, ide_model, ide_lre, derivatives_info, info, options_ident] = identification_analysis(params,indx,indexo,options_ident,dataset_,dataset_info, prior_exist,name_tex,init,tittxt,bounds)
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% function [ide_hess, ide_moments, ide_model, ide_lre, derivatives_info, info] = identification_analysis(params,indx,indexo,options_ident,data_info, prior_exist,name_tex,init,analyis_type)
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% given the parameter vector params, wraps all identification analyses
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%
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% INPUTS
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% o params [array] parameter values for identification checks
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% o indx [array] index of estimated parameters
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% o indexo [array] index of estimated shocks
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% o options_ident [structure] identification options
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% o dataset_ [structure] the dataset after required transformation
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% o dataset_info [structure] Various informations about the dataset (descriptive statistics and missing observations) info for Kalman Filter
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% o prior_exist [integer]
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% =1 when prior exists and indentification is checked only for estimated params and shocks
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% =0 when prior is not defined and indentification is checked for all params and shocks
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% o name_tex [char] list of tex names
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% o init [integer] flag for initialization of persistent vars
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% o tittxt [string] string indicating the title text for
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% graphs and figures
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%
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% OUTPUTS
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% o ide_hess [structure] identification results using Asymptotic Hessian
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% o ide_moments [structure] identification results using theoretical moments
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% o ide_model [structure] identification results using reduced form solution
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% o ide_lre [structure] identification results using LRE model
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% o derivatives_info [structure] info about analytic derivs
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% o info output from dynare resolve
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%
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% SPECIAL REQUIREMENTS
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% None
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% Copyright (C) 2008-2018 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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global oo_ M_ options_ bayestopt_ estim_params_
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persistent indH indJJ indLRE
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nparam=length(params);
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np=length(indx);
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offset=nparam-np;
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if ~isempty(estim_params_)
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M_ = set_all_parameters(params,estim_params_,M_);
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end
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nlags = options_ident.ar;
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useautocorr = options_ident.useautocorr;
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advanced = options_ident.advanced;
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replic = options_ident.replic;
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periods = options_ident.periods;
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max_dim_cova_group = options_ident.max_dim_cova_group;
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normalize_jacobians = options_ident.normalize_jacobians;
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kron_flag = options_ident.analytic_derivation_mode;
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[I,J]=find(M_.lead_lag_incidence');
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ide_hess = struct();
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ide_moments = struct();
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ide_model = struct();
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ide_lre = struct();
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derivatives_info = struct();
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[A,B,ys,info,M_,options_,oo_] = dynare_resolve(M_,options_,oo_);
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if info(1)==0
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oo0=oo_;
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tau=[oo_.dr.ys(oo_.dr.order_var); vec(A); dyn_vech(B*M_.Sigma_e*B')];
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yy0=oo_.dr.ys(I);
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[residual, g1 ] = feval([M_.fname,'.dynamic'],yy0, ...
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repmat(oo_.exo_steady_state',[M_.maximum_exo_lag+M_.maximum_exo_lead+1]), M_.params, ...
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oo_.dr.ys, 1);
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vg1 = [oo_.dr.ys(oo_.dr.order_var); vec(g1)];
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[JJ, H, gam, gp, dA, dOm, dYss] = getJJ(A, B, estim_params_, M_,oo0,options_,kron_flag,indx,indexo,bayestopt_.mf2,nlags,useautocorr);
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derivatives_info.DT=dA;
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derivatives_info.DOm=dOm;
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derivatives_info.DYss=dYss;
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if init
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indJJ = (find(max(abs(JJ'),[],1)>1.e-8));
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if isempty(indJJ) && any(any(isnan(JJ)))
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error('There are NaN in the JJ matrix. Please check whether your model has units roots and you forgot to set diffuse_filter=1.' )
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elseif any(any(isnan(gam)))
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error('There are NaN''s in the theoretical moments: make sure that for non-stationary models stationary transformations of non-stationary observables are used for checking identification. [TIP: use first differences].')
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end
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while length(indJJ)<nparam && nlags<10
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disp('The number of moments with non-zero derivative is smaller than the number of parameters')
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disp(['Try increasing ar = ', int2str(nlags+1)])
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nlags=nlags+1;
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[JJ, H, gam, gp, dA, dOm, dYss] = getJJ(A, B, estim_params_, M_,oo0,options_,kron_flag,indx,indexo,bayestopt_.mf2,nlags,useautocorr);
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derivatives_info.DT=dA;
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derivatives_info.DOm=dOm;
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derivatives_info.DYss=dYss;
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options_.ar=nlags;
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options_ident.ar=nlags;
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indJJ = (find(max(abs(JJ'),[],1)>1.e-8));
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end
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if length(indJJ)<nparam
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disp('The number of moments with non-zero derivative is smaller than the number of parameters')
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disp('up to 10 lags: check your model')
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disp('Either further increase ar or reduce the list of estimated parameters')
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error('identification_analysis: there are not enough moments and too many parameters'),
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end
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indH = (find(max(abs(H'),[],1)>1.e-8));
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indLRE = (find(max(abs(gp'),[],1)>1.e-8));
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end
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TAU(:,1)=tau(indH);
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LRE(:,1)=vg1(indLRE);
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GAM(:,1)=gam(indJJ);
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siJ = (JJ(indJJ,:));
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siH = (H(indH,:));
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siLRE = (gp(indLRE,:));
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ide_strength_J=NaN(1,nparam);
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ide_strength_J_prior=NaN(1,nparam);
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if init
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ide_uncert_unnormaliz = NaN(1,nparam);
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if prior_exist
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offset_prior=0;
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if ~isempty(estim_params_.var_exo)
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normaliz_prior_std = bayestopt_.p2(1:estim_params_.nvx)'; % normalize with prior standard deviation
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offset_prior=offset_prior+estim_params_.nvx+estim_params_.nvn;
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else
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normaliz_prior_std=[];
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end
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if ~isempty(estim_params_.corrx)
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normaliz_prior_std = [normaliz_prior_std bayestopt_.p2(offset_prior+1:offset_prior+estim_params_.ncx)']; % normalize with prior standard deviation
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offset_prior=offset_prior+estim_params_.ncx+estim_params_.ncn;
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end
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if ~isempty(estim_params_.param_vals)
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normaliz_prior_std = [normaliz_prior_std bayestopt_.p2(offset_prior+1:offset_prior+estim_params_.np)']; % normalize with prior standard deviation
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end
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% normaliz = max([normaliz; normaliz1]);
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% normaliz1(isinf(normaliz1)) = 1;
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else
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normaliz_prior_std = NaN(1,nparam);
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end
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try
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options_.irf = 0;
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options_.noprint = 1;
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options_.order = 1;
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options_.SpectralDensity.trigger = 0;
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options_.periods = periods+100;
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if options_.kalman_algo > 2
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options_.kalman_algo = 1;
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end
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analytic_derivation = options_.analytic_derivation;
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options_.analytic_derivation = -2;
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info = stoch_simul(options_.varobs);
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dataset_ = dseries(oo_.endo_simul(options_.varobs_id,100+1:end)',dates('1Q1'), options_.varobs);
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derivatives_info.no_DLIK=1;
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bounds = prior_bounds(bayestopt_, options_.prior_trunc); %reset bounds as lb and ub must only be operational during mode-finding
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[fval,info,cost_flag,DLIK,AHess,ys,trend_coeff,M_,options_,bayestopt_,oo_] = dsge_likelihood(params',dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,bounds,oo_,derivatives_info);
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% fval = DsgeLikelihood(xparam1,data_info,options_,M_,estim_params_,bayestopt_,oo_);
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options_.analytic_derivation = analytic_derivation;
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AHess=-AHess;
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if min(eig(AHess))<-1.e-10
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error('identification_analysis: Analytic Hessian is not positive semi-definite!')
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end
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% chol(AHess);
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ide_hess.AHess= AHess;
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deltaM = sqrt(diag(AHess));
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iflag=any((deltaM.*deltaM)==0);
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tildaM = AHess./((deltaM)*(deltaM'));
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if iflag || rank(AHess)>rank(tildaM)
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[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(AHess, 1);
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else
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[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(tildaM, 1);
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end
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indok = find(max(ide_hess.indno,[],1)==0);
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cparam(indok,indok) = inv(AHess(indok,indok));
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ide_uncert_unnormaliz(indok) = sqrt(diag(cparam(indok,indok)))';
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cmm = NaN(size(siJ,1),size(siJ,1));
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ind1=find(ide_hess.ind0);
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cmm = siJ(:,ind1)*((AHess(ind1,ind1))\siJ(:,ind1)');
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temp1=((AHess(ind1,ind1))\siH(:,ind1)');
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diag_chh=sum(siH(:,ind1)'.*temp1)';
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% chh = siH(:,ind1)*((AHess(ind1,ind1))\siH(:,ind1)');
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ind1=ind1(ind1>offset);
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clre = siLRE(:,ind1-offset)*((AHess(ind1,ind1))\siLRE(:,ind1-offset)');
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rhoM=sqrt(1./diag(inv(tildaM(indok,indok))));
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% deltaM = deltaM.*abs(params');
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flag_score=1;
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catch
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% replic = max([replic, nparam*(nparam+1)/2*10]);
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replic = max([replic, length(indJJ)*3]);
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cmm = simulated_moment_uncertainty(indJJ, periods, replic,options_,M_,oo_);
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% [V,D,W]=eig(cmm);
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sd=sqrt(diag(cmm));
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cc=cmm./(sd*sd');
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if isoctave || matlab_ver_less_than('8.3')
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[V,D]=eig(cc);
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%fix for older Matlab versions that do not support computing left eigenvalues, see http://mathworks.com/help/releases/R2012b/matlab/ref/eig.html
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[W,~] = eig(cc.');
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W = conj(W);
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else
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[V,D,W]=eig(cc);
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end
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id=find(diag(D)>1.e-8);
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siTMP=siJ./repmat(sd,[1 nparam]);
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MIM=(siTMP'*V(:,id))*(D(id,id)\(W(:,id)'*siTMP));
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clear siTMP;
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% MIM=siJ(:,indok)'*(cmm\siJ(:,indok));
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% look for independent moments!
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% % % sd=sqrt(diag(cmm));
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% % % cc=cmm./(sd*sd');
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% % % ix=[];
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% % % for jc=1:length(cmm),
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% % % jcheck=find(abs(cc(:,jc))>(1-1.e-6));
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% % % ix=[ix; jcheck(jcheck>jc)];
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% % % end
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% % % iy=find(~ismember([1:length(cmm)],ix));
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% % % indJJ=indJJ(iy);
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% % % GAM=GAM(iy);
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% % % cmm=cmm(iy,iy);
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% % % siJ = (JJ(indJJ,:));
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% % % MIM=siJ'*(cmm\siJ);
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ide_hess.AHess= MIM;
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deltaM = sqrt(diag(MIM));
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iflag=any((deltaM.*deltaM)==0);
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tildaM = MIM./((deltaM)*(deltaM'));
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if iflag || rank(MIM)>rank(tildaM)
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[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(MIM, 1);
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else
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[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(tildaM, 1);
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end
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indok = find(max(ide_hess.indno,[],1)==0);
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% rhoM=sqrt(1-1./diag(inv(tildaM)));
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% rhoM=(1-1./diag(inv(tildaM)));
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ind1=find(ide_hess.ind0);
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temp1=((MIM(ind1,ind1))\siH(:,ind1)');
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diag_chh=sum(siH(:,ind1)'.*temp1)';
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% chh = siH(:,ind1)*((MIM(ind1,ind1))\siH(:,ind1)');
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ind1=ind1(ind1>offset);
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clre = siLRE(:,ind1-offset)*((MIM(ind1,ind1))\siLRE(:,ind1-offset)');
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if ~isempty(indok)
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rhoM(indok)=sqrt(1./diag(inv(tildaM(indok,indok))));
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ide_uncert_unnormaliz(indok) = (sqrt(diag(inv(tildaM(indok,indok))))./deltaM(indok))'; %sqrt(diag(inv(MIM(indok,indok))))';
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end
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% deltaM = deltaM.*abs(params')
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flag_score=0;
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end
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ide_strength_J(indok) = (1./(ide_uncert_unnormaliz(indok)'./abs(params(indok)')));
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ide_strength_J_prior(indok) = (1./(ide_uncert_unnormaliz(indok)'./normaliz_prior_std(indok)'));
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%ide_strength_J(params==0)=1./ide_uncert_unnormaliz(params==0)';
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sensitivity_zero_pos=find(isinf(deltaM));
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deltaM_prior = deltaM.*abs(normaliz_prior_std');
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deltaM = deltaM.*abs(params');
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%deltaM(params==0)=deltaM_prior(params==0);
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quant = siJ./repmat(sqrt(diag(cmm)),1,nparam);
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if size(quant,1)==1
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siJnorm = abs(quant).*normaliz_prior_std;
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else
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siJnorm = vnorm(quant).*normaliz_prior_std;
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end
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% siJnorm = vnorm(siJ(inok,:)).*normaliz;
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quant=[];
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% inok = find((abs(TAU)<1.e-8));
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% isok = find((abs(TAU)>=1.e-8));
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% quant(isok,:) = siH(isok,:)./repmat(TAU(isok,1),1,nparam);
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% quant(inok,:) = siH(inok,:)./repmat(mean(abs(TAU)),length(inok),nparam);
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% quant = siH./repmat(sqrt(diag(chh)),1,nparam);
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iy = find(diag_chh);
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indH=indH(iy);
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siH=siH(iy,:);
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if ~isempty(iy)
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quant = siH./repmat(sqrt(diag_chh(iy)),1,nparam);
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if size(quant,1)==1
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siHnorm = abs(quant).*normaliz_prior_std;
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else
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siHnorm = vnorm(quant).*normaliz_prior_std;
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end
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else
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siHnorm = [];
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end
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% siHnorm = vnorm(siH./repmat(TAU,1,nparam)).*normaliz;
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quant=[];
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% inok = find((abs(LRE)<1.e-8));
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% isok = find((abs(LRE)>=1.e-8));
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% quant(isok,:) = siLRE(isok,:)./repmat(LRE(isok,1),1,np);
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% quant(inok,:) = siLRE(inok,:)./repmat(mean(abs(LRE)),length(inok),np);
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diag_clre = diag(clre);
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iy = find(diag_clre);
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indLRE=indLRE(iy);
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siLRE=siLRE(iy,:);
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if ~isempty(iy)
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quant = siLRE./repmat(sqrt(diag_clre(iy)),1,np);
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if size(quant,1)==1
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siLREnorm = abs(quant).*normaliz_prior_std(offset+1:end);
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else
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siLREnorm = vnorm(quant).*normaliz_prior_std(offset+1:end);
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end
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else
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siLREnorm=[];
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end
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% siLREnorm = vnorm(siLRE./repmat(LRE,1,nparam-offset)).*normaliz(offset+1:end);
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ide_hess.ide_strength_J=ide_strength_J;
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ide_hess.ide_strength_J_prior=ide_strength_J_prior;
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ide_hess.deltaM=deltaM;
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ide_hess.deltaM_prior=deltaM_prior;
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ide_hess.sensitivity_zero_pos=sensitivity_zero_pos;
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ide_hess.identified_parameter_indices=indok;
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ide_moments.siJnorm=siJnorm;
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ide_model.siHnorm=siHnorm;
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ide_lre.siLREnorm=siLREnorm;
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ide_hess.flag_score=flag_score;
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end
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if normalize_jacobians
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normH = max(abs(siH)')';
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normH = normH(:,ones(nparam,1));
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normJ = max(abs(siJ)')';
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normJ = normJ(:,ones(nparam,1));
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normLRE = max(abs(siLRE)')';
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normLRE = normLRE(:,ones(size(gp,2),1));
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else
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normH = 1;
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normJ = 1;
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normLRE = 1;
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end
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ide_moments.indJJ=indJJ;
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ide_model.indH=indH;
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ide_lre.indLRE=indLRE;
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ide_moments.siJ=siJ;
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ide_model.siH=siH;
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ide_lre.siLRE=siLRE;
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ide_moments.GAM=GAM;
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ide_model.TAU=TAU;
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ide_lre.LRE=LRE;
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% [ide_checks.idemodel_Mco, ide_checks.idemoments_Mco, ide_checks.idelre_Mco, ...
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% ide_checks.idemodel_Pco, ide_checks.idemoments_Pco, ide_checks.idelre_Pco, ...
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% ide_checks.idemodel_cond, ide_checks.idemoments_cond, ide_checks.idelre_cond, ...
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% ide_checks.idemodel_ee, ide_checks.idemoments_ee, ide_checks.idelre_ee, ...
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% ide_checks.idemodel_ind, ide_checks.idemoments_ind, ...
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% ide_checks.idemodel_indno, ide_checks.idemoments_indno, ...
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% ide_checks.idemodel_ino, ide_checks.idemoments_ino] = ...
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% identification_checks(H(indH,:)./normH(:,ones(nparam,1)),JJ(indJJ,:)./normJ(:,ones(nparam,1)), gp(indLRE,:)./normLRE(:,ones(size(gp,2),1)));
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[ide_moments.cond, ide_moments.ind0, ide_moments.indno, ide_moments.ino, ide_moments.Mco, ide_moments.Pco, ide_moments.jweak, ide_moments.jweak_pair] = ...
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identification_checks(JJ(indJJ,:)./normJ, 0);
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[ide_model.cond, ide_model.ind0, ide_model.indno, ide_model.ino, ide_model.Mco, ide_model.Pco, ide_model.jweak, ide_model.jweak_pair] = ...
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identification_checks(H(indH,:)./normH, 0);
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[ide_lre.cond, ide_lre.ind0, ide_lre.indno, ide_lre.ino, ide_lre.Mco, ide_lre.Pco, ide_lre.jweak, ide_lre.jweak_pair] = ...
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identification_checks(gp(indLRE,:)./normLRE, 0);
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normJ=1;
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[U, S, V]=svd(JJ(indJJ,:)./normJ,0);
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S=diag(S);
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S=[S;zeros(size(JJ,2)-length(indJJ),1)];
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if nparam>8
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ide_moments.S = S([1:4, end-3:end]);
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|
ide_moments.V = V(:,[1:4, end-3:end]);
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|
else
|
|
ide_moments.S = S;
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|
ide_moments.V = V;
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|
end
|
|
indok = find(max(ide_moments.indno,[],1)==0);
|
|
if advanced
|
|
[ide_moments.pars, ide_moments.cosnJ] = ident_bruteforce(JJ(indJJ,:)./normJ,max_dim_cova_group,options_.TeX,name_tex,tittxt);
|
|
end
|
|
end
|