Merge branch 'optimizer' of git.dynare.org:JohannesPfeifer/dynare
commit
3e7c0b1eef
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@ -274,7 +274,7 @@ if ~isequal(options_.mode_compute,0) && ~options_.mh_posterior_mode_estimation
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if compute_hessian
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crit = options_.newrat.tolerance.f;
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newratflag = newratflag>0;
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hh = reshape(mr_hessian(xparam1,objective_function,fval,newratflag,crit,new_rat_hess_info,[bounds.lb bounds.ub],bayestopt_.p2,dataset_, dataset_info, options_,M_,estim_params_,bayestopt_,bounds,oo_), nx, nx);
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hh = reshape(mr_hessian(xparam1,objective_function,fval,newratflag,crit,new_rat_hess_info,[bounds.lb bounds.ub],bayestopt_.p2,0,dataset_, dataset_info, options_,M_,estim_params_,bayestopt_,bounds,oo_), nx, nx);
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end
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options_.kalman_algo = kalman_algo0;
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end
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@ -129,7 +129,6 @@ else
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done=0;
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factor=3;
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shrink=1;
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lambdaMin=0;
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lambdaMax=inf;
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lambdaPeak=0;
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fPeak=f0;
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@ -1,15 +1,15 @@
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function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1, hess_info] = mr_hessian(x,func,penalty,hflag,htol0,hess_info,bounds,prior_std,varargin)
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% function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1, hess_info] = mr_hessian(x,func,penalty,hflag,htol0,hess_info,bounds,prior_std,varargin)
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function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1, hess_info] = mr_hessian(x,func,penalty,hflag,htol0,hess_info,bounds,prior_std,Save_files,varargin)
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% function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1, hess_info] = mr_hessian(x,func,penalty,hflag,htol0,hess_info,bounds,prior_std,Save_files,varargin)
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% numerical gradient and Hessian, with 'automatic' check of numerical
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% error
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%
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% adapted from Michel Juillard original routine hessian.m
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%
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% Inputs:
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% - x parameter values
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% - func function handle. The function must give two outputs:
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% the log-likelihood AND the single contributions at times t=1,...,T
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% of the log-likelihood to compute outer product gradient
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% - x parameter values
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% - penalty penalty due to error code
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% - hflag 0: Hessian computed with outer product gradient, one point
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% increments for partial derivatives in gradients
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@ -26,6 +26,7 @@ function [hessian_mat, gg, htol1, ihh, hh_mat0, hh1, hess_info] = mr_hessian(x,f
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% computation of Hessian
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% - bounds prior bounds of parameters
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% - prior_std prior standard devation of parameters (can be NaN)
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% - Save_files indicator whether files should be saved
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% - varargin other inputs
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% e.g. in dsge_likelihood
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% varargin{1} --> DynareDataset
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@ -99,11 +100,7 @@ while i<n
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h10=hess_info.h1(i);
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hcheck=0;
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xh1(i)=x(i)+hess_info.h1(i);
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try
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[fx,exit_flag,ffx]=penalty_objective_function(xh1,func,penalty,varargin{:});
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catch
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fx=1.e8;
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end
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[fx,exit_flag,ffx]=penalty_objective_function(xh1,func,penalty,varargin{:});
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it=1;
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dx=(fx-f0);
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ic=0;
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@ -120,21 +117,13 @@ while i<n
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hess_info.h1(i) = min(hess_info.h1(i),0.5*hmax(i));
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hess_info.h1(i) = max(hess_info.h1(i),1.e-10);
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xh1(i)=x(i)+hess_info.h1(i);
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try
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[fx,exit_flag,ffx]=penalty_objective_function(xh1,func,penalty,varargin{:});
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catch
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fx=1.e8;
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end
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[fx,exit_flag,ffx]=penalty_objective_function(xh1,func,penalty,varargin{:});
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end
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if abs(dx(it))>(3*hess_info.htol)
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hess_info.h1(i)= hess_info.htol/abs(dx(it))*hess_info.h1(i);
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hess_info.h1(i) = max(hess_info.h1(i),1e-10);
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xh1(i)=x(i)+hess_info.h1(i);
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try
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[fx,exit_flag,ffx]=penalty_objective_function(xh1,func,penalty,varargin{:});
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catch
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fx=1.e8;
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end
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[fx,exit_flag,ffx]=penalty_objective_function(xh1,func,penalty,varargin{:});
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iter=0;
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while (fx-f0)==0 && iter<50
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hess_info.h1(i)= hess_info.h1(i)*2;
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@ -188,7 +177,7 @@ gg=(f1'-f_1')./(2.*hess_info.h1);
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if outer_product_gradient
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if hflag==2
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gg=(f1'-f_1')./(2.*hess_info.h1);
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% full numerical Hessian
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hessian_mat = zeros(size(f0,1),n*n);
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for i=1:n
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if i > 1
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@ -209,19 +198,17 @@ if outer_product_gradient
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xh1(j)=x(j);
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xh_1(i)=x(i);
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xh_1(j)=x(j);
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j=j+1;
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end
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i=i+1;
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end
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elseif hflag==1
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% full numerical 2nd order derivs only in diagonal
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hessian_mat = zeros(size(f0,1),n*n);
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for i=1:n
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dum = (f1(:,i)+f_1(:,i)-2*f0)./(hess_info.h1(i)*h_1(i));
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if dum>eps
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hessian_mat(:,(i-1)*n+i)=dum;
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else
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hessian_mat(:,(i-1)*n+i)=max(eps, gg(i)^2);
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end
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hessian_mat(:,(i-1)*n+i)=dum;
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if any(dum<=eps)
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hessian_mat(dum<=eps,(i-1)*n+i)=max(eps, gg(i)^2);
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end
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end
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end
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@ -230,26 +217,27 @@ if outer_product_gradient
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hh_mat0=ggh'*ggh; % outer product hessian
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A=diag(2.*hess_info.h1); % rescaling matrix
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% igg=inv(hh_mat); % inverted rescaled outer product hessian
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ihh=A'*(hh_mat\A); % inverted outer product hessian
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ihh=A'*(hh_mat\A); % inverted outer product hessian (based on rescaling)
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if hflag>0 && min(eig(reshape(hessian_mat,n,n)))>0
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hh0 = A*reshape(hessian_mat,n,n)*A'; %rescaled second order derivatives
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hh = reshape(hessian_mat,n,n); %rescaled second order derivatives
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hh = reshape(hessian_mat,n,n); %second order derivatives
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sd0=sqrt(diag(hh0)); %rescaled 'standard errors' using second order derivatives
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sd=sqrt(diag(hh_mat)); %rescaled 'standard errors' using outer product
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hh_mat=hh_mat./(sd*sd').*(sd0*sd0'); %rescaled inverse outer product with 'true' std's
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igg=inv(hh_mat); % rescaled outer product hessian with 'true' std's
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ihh=A'*(hh_mat\A); % inverted outer product hessian
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hh_mat0=inv(A)'*hh_mat*inv(A); % outer product hessian with 'true' std's
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ihh=A'*(hh_mat\A); % update inverted outer product hessian with 'true' std's
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sd=sqrt(diag(ihh)); %standard errors
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sdh=sqrt(1./diag(hh)); %diagonal standard errors
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for j=1:length(sd)
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% some heuristic normalizations of the standard errors that
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% avoid numerical issues in outer product
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sd0(j,1)=min(prior_std(j), sd(j)); %prior std
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sd0(j,1)=10^(0.5*(log10(sd0(j,1))+log10(sdh(j,1))));
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end
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inv_A=inv(A);
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ihh=ihh./(sd*sd').*(sd0*sd0'); %inverse outer product with modified std's
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igg=inv(A)'*ihh*inv(A); % inverted rescaled outer product hessian with modified std's
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hh_mat=inv(igg); % outer product rescaled hessian with modified std's
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hh_mat0=inv(A)'*hh_mat*inv(A); % outer product hessian with modified std's
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igg=inv_A'*ihh*inv_A; % inverted rescaled outer product hessian with modified std's
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% hh_mat=inv(igg); % outer product rescaled hessian with modified std's
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hh_mat0=inv_A'/igg*inv_A; % outer product hessian with modified std's
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% sd0=sqrt(1./diag(hh0)); %rescaled 'standard errors' using second order derivatives
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% sd=sqrt(diag(igg)); %rescaled 'standard errors' using outer product
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% igg=igg./(sd*sd').*(sd0*sd0'); %rescaled inverse outer product with 'true' std's
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@ -267,7 +255,9 @@ if outer_product_gradient
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hessian_mat=hh_mat0(:);
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end
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hh1=hess_info.h1;
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save hess.mat hessian_mat
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if Save_files
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save('hess.mat','hessian_mat')
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end
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else
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hessian_mat=[];
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ihh=[];
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@ -70,7 +70,7 @@ nx=length(x);
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xparam1=x;
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%ftol0=1.e-6;
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htol_base = max(1.e-7, ftol0);
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flagit=0; % mode of computation of hessian in each iteration
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flagit=0; % mode of computation of hessian in each iteration; hard-coded outer-product of gradients as it performed best in tests
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ftol=ftol0;
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gtol=1.e-3;
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htol=htol_base;
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@ -84,13 +84,17 @@ end
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% func0 = str2func([func2str(func0),'_hh']);
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% func0 = func0;
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[fval0,exit_flag,gg,hh]=penalty_objective_function(x,func0,penalty,varargin{:});
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if ~exit_flag
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disp_verbose('Bad initial parameter.',Verbose)
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return
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end
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fval=fval0;
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% initialize mr_gstep and mr_hessian
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outer_product_gradient=1;
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if isempty(hh)
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[dum, gg, htol0, igg, hhg, h1, hess_info]=mr_hessian(x,func0,penalty,flagit,htol,hess_info,bounds,prior_std,varargin{:});
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[dum, gg, htol0, igg, hhg, h1, hess_info]=mr_hessian(x,func0,penalty,flagit,htol,hess_info,bounds,prior_std,Save_files,varargin{:});
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if isempty(dum)
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outer_product_gradient=0;
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igg = 1e-4*eye(nx);
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@ -117,15 +121,16 @@ else
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h1=[];
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end
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H = igg;
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disp_verbose(['Gradient norm ',num2str(norm(gg))],Verbose)
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ee=eig(hh);
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disp_verbose(['Minimum Hessian eigenvalue ',num2str(min(ee))],Verbose)
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disp_verbose(['Maximum Hessian eigenvalue ',num2str(max(ee))],Verbose)
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if Verbose
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disp_eigenvalues_gradient(gg,hh);
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end
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g=gg;
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check=0;
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if max(eig(hh))<0
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disp_verbose('Negative definite Hessian! Local maximum!',Verbose)
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pause
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if Verbose
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if max(eig(hh))<0
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disp('Negative definite Hessian! Local maximum!')
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pause
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end
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end
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if Save_files
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save('m1.mat','x','hh','g','hhg','igg','fval0')
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@ -135,7 +140,9 @@ igrad=1;
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igibbs=1;
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inx=eye(nx);
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jit=0;
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nig=[];
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if Save_files
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nig=[];
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end
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ig=ones(nx,1);
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ggx=zeros(nx,1);
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while norm(gg)>gtol && check==0 && jit<nit
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@ -156,22 +163,25 @@ while norm(gg)>gtol && check==0 && jit<nit
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fval=fval1;
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x0=x01;
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end
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if length(find(ig))<nx
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ggx=ggx*0;
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ggx(find(ig))=gg(find(ig));
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ig_pos=find(ig);
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if length(ig_pos)<nx
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ggx=ggx*0;
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ggx(ig_pos)=gg(ig_pos);
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if analytic_derivation || ~outer_product_gradient
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hhx=hh;
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else
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hhx = reshape(dum,nx,nx);
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end
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iggx=eye(length(gg));
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iggx(find(ig),find(ig)) = inv( hhx(find(ig),find(ig)) );
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iggx(ig_pos,ig_pos) = inv( hhx(ig_pos,ig_pos) );
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[fvala,x0,fc,retcode] = csminit1(func0,x0,penalty,fval,ggx,0,iggx,Verbose,varargin{:});
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end
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x0 = check_bounds(x0,bounds);
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[fvala, x0, ig] = mr_gstep(h1,x0,bounds,func0,penalty,htol0,Verbose,Save_files,gradient_epsilon, parameter_names,varargin{:});
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x0 = check_bounds(x0,bounds);
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nig=[nig ig];
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if Save_files
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nig=[nig ig];
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end
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disp_verbose('Sequence of univariate steps!!',Verbose)
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fval=fvala;
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if (fval0(icount)-fval)<ftol && flagit==0
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@ -208,7 +218,7 @@ while norm(gg)>gtol && check==0 && jit<nit
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if flagit==2
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hh=hh0;
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elseif flagg>0
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[dum, gg, htol0, igg, hhg, h1, hess_info]=mr_hessian(xparam1,func0,penalty,flagg,ftol0,hess_info,bounds,prior_std,varargin{:});
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[dum, gg, htol0, igg, hhg, h1, hess_info]=mr_hessian(xparam1,func0,penalty,flagg,ftol0,hess_info,bounds,prior_std,Save_files,varargin{:});
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if flagg==2
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hh = reshape(dum,nx,nx);
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ee=eig(hh);
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@ -220,15 +230,14 @@ while norm(gg)>gtol && check==0 && jit<nit
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end
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end
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end
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disp_verbose(['Actual dxnorm ',num2str(norm(x(:,end)-x(:,end-1)))],Verbose)
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disp_verbose(['FVAL ',num2str(fval)],Verbose)
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disp_verbose(['Improvement ',num2str(fval0(icount)-fval)],Verbose)
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disp_verbose(['Ftol ',num2str(ftol)],Verbose)
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disp_verbose(['Htol ',num2str(max(htol0))],Verbose)
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disp_verbose(['Gradient norm ',num2str(norm(gg))],Verbose)
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ee=eig(hh);
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disp_verbose(['Minimum Hessian eigenvalue ',num2str(min(ee))],Verbose)
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disp_verbose(['Maximum Hessian eigenvalue ',num2str(max(ee))],Verbose)
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if Verbose
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disp(['Actual dxnorm ',num2str(norm(x(:,end)-x(:,end-1)))])
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disp(['FVAL ',num2str(fval)])
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disp(['Improvement ',num2str(fval0(icount)-fval)])
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disp(['Ftol ',num2str(ftol)])
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disp(['Htol ',num2str(max(htol0))])
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disp_eigenvalues_gradient(gg,hh);
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end
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g(:,icount+1)=gg;
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else
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df = fval0(icount)-fval;
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@ -248,7 +257,7 @@ while norm(gg)>gtol && check==0 && jit<nit
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save('m1.mat','x','fval0','nig')
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end
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end
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[dum, gg, htol0, igg, hhg, h1, hess_info]=mr_hessian(xparam1,func0,penalty,flagit,htol,hess_info,bounds,prior_std,varargin{:});
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[dum, gg, htol0, igg, hhg, h1, hess_info]=mr_hessian(xparam1,func0,penalty,flagit,htol,hess_info,bounds,prior_std,Save_files,varargin{:});
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if isempty(dum)
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outer_product_gradient=0;
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end
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@ -280,13 +289,11 @@ while norm(gg)>gtol && check==0 && jit<nit
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hhg=hh;
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H = inv(hh);
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end
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disp_verbose(['Gradient norm ',num2str(norm(gg))],Verbose)
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ee=eig(hh);
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disp_verbose(['Minimum Hessian eigenvalue ',num2str(min(ee))],Verbose)
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disp_verbose(['Maximum Hessian eigenvalue ',num2str(max(ee))],Verbose)
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if max(eig(hh))<0
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disp_verbose('Negative definite Hessian! Local maximum!',Verbose)
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pause(1)
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if Verbose
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if max(eig(hh))<0
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disp('Negative definite Hessian! Local maximum!')
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pause(1)
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end
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end
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t=toc(tic1);
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disp_verbose(['Elapsed time for iteration ',num2str(t),' s.'],Verbose)
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@ -334,3 +341,10 @@ inx = find(x<=bounds(:,1));
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if ~isempty(inx)
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x(inx) = bounds(inx,1)+eps;
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end
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function ee=disp_eigenvalues_gradient(gg,hh)
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disp(['Gradient norm ',num2str(norm(gg))])
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ee=eig(hh);
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disp(['Minimum Hessian eigenvalue ',num2str(min(ee))])
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disp(['Maximum Hessian eigenvalue ',num2str(max(ee))])
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