337 lines
12 KiB
Matlab
337 lines
12 KiB
Matlab
function [xparam1, hh, gg, fval, igg, hess_info] = newrat(func0, x, bounds, analytic_derivation, ftol0, nit, flagg, Verbose, Save_files, hess_info, prior_std, gradient_epsilon, parameter_names, varargin)
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% [xparam1, hh, gg, fval, igg, hess_info] = newrat(func0, x, bounds, analytic_derivation, ftol0, nit, flagg, Verbose, Save_files, hess_info, gradient_epsilon, parameter_names, varargin)
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%
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% Optimiser with outer product gradient and with sequences of univariate steps
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% uses Chris Sims subroutine for line search
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%
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% Inputs:
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% - func0 name of the function that also outputs 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 starting guess
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% - bounds prior bounds of parameters
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% - analytic_derivation 1 if analytic derivatives, 0 otherwise
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% - ftol0 termination criterion for function change
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% - nit maximum number of iterations
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% - flagg Indicator how to compute final Hessian (In each iteration, Hessian is computed with outer product gradient)
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% 0: final Hessian computed with outer product gradient
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% 1: final 'mixed' Hessian: diagonal elements computed with
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% numerical second order derivatives with correlation structure
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% as from outer product gradient
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% 2: full numerical Hessian
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% - Verbose 1 if explicit output is requested
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% - Save_files 1 if intermediate output is to be saved
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% - hess_info structure storing the step sizes for
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% computation of Hessian
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% - prior_std prior standard devation of parameters (can be NaN);
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% passed to mr_hessian
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% - gradient_epsilon [double] step size in gradient
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% - parameter_names [cell] names of parameters for error messages
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% - varargin other inputs
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% e.g. in dsge_likelihood and others:
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% varargin{1} --> DynareDataset
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% varargin{2} --> DatasetInfo
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% varargin{3} --> DynareOptions
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% varargin{4} --> Model
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% varargin{5} --> EstimatedParameters
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% varargin{6} --> BayesInfo
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% varargin{7} --> Bounds
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% varargin{8} --> DynareResults
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%
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% Outputs
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% - xparam1 parameter vector at optimum
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% - hh hessian
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% - gg gradient
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% - fval function value
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% - igg inverted outer product hessian
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% - hess_info structure with updated step length
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% Copyright (C) 2004-2017 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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% initialize variable penalty
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penalty = 1e8;
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icount=0;
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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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ftol=ftol0;
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gtol=1.e-3;
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htol=htol_base;
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htol0=htol_base;
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% force fcn, grad to function handle
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if ischar(func0)
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func0 = str2func(func0);
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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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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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if isempty(dum)
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outer_product_gradient=0;
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igg = 1e-4*eye(nx);
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else
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hh0 = reshape(dum,nx,nx);
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hh=hhg;
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if min(eig(hh0))<0
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hh0=hhg; %generalized_cholesky(hh0);
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elseif flagit==2
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hh=hh0;
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igg=inv(hh);
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end
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end
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if max(htol0)>htol
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skipline()
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disp_verbose('Numerical noise in the likelihood',Verbose)
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disp_verbose('Tolerance has to be relaxed',Verbose)
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skipline()
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end
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else
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hh0=hh;
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hhg=hh;
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igg=inv(hh);
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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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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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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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end
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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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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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jit=jit+1;
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tic1 = tic;
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icount=icount+1;
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penalty = fval0(icount);
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disp_verbose([' '],Verbose)
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disp_verbose(['Iteration ',num2str(icount)],Verbose)
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[fval,x0,fc,retcode] = csminit1(func0,xparam1,penalty,fval0(icount),gg,0,H,Verbose,varargin{:});
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if igrad
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[fval1,x01,fc,retcode1] = csminit1(func0,x0,penalty,fval,gg,0,inx,Verbose,varargin{:});
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if (fval-fval1)>1
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disp_verbose('Gradient step!!',Verbose)
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else
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igrad=0;
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end
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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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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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[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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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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disp_verbose('Try diagonal Hessian',Verbose)
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ihh=diag(1./(diag(hhg)));
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[fval2,x0,fc,retcode2] = csminit1(func0,x0,penalty,fval,gg,0,ihh,Verbose,varargin{:});
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x0 = check_bounds(x0,bounds);
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if (fval-fval2)>=ftol
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disp_verbose('Diagonal Hessian successful',Verbose)
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end
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fval=fval2;
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end
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if (fval0(icount)-fval)<ftol && flagit==0
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disp_verbose('Try gradient direction',Verbose)
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ihh0=inx.*1.e-4;
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[fval3,x0,fc,retcode3] = csminit1(func0,x0,penalty,fval,gg,0,ihh0,Verbose,varargin{:});
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x0 = check_bounds(x0,bounds);
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if (fval-fval3)>=ftol
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disp_verbose('Gradient direction successful',Verbose)
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end
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fval=fval3;
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end
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xparam1=x0;
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x(:,icount+1)=xparam1;
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fval0(icount+1)=fval;
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if (fval0(icount)-fval)<ftol
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disp_verbose('No further improvement is possible!',Verbose)
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check=1;
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if analytic_derivation
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[fvalx,exit_flag,gg,hh]=penalty_objective_function(xparam1,func0,penalty,varargin{:});
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hhg=hh;
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H = inv(hh);
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else
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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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if flagg==2
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hh = reshape(dum,nx,nx);
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ee=eig(hh);
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if min(ee)<0
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hh=hhg;
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end
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else
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hh=hhg;
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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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g(:,icount+1)=gg;
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else
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df = fval0(icount)-fval;
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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(df)],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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htol=htol_base;
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if norm(x(:,icount)-xparam1)>1.e-12 && analytic_derivation==0
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try
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if Save_files
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save('m1.mat','x','fval0','nig','-append')
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end
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catch
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if Save_files
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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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if isempty(dum)
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outer_product_gradient=0;
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end
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if max(htol0)>htol
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skipline()
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disp_verbose('Numerical noise in the likelihood',Verbose)
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disp_verbose('Tolerance has to be relaxed',Verbose)
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skipline()
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end
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if ~outer_product_gradient
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H = bfgsi1(H,gg-g(:,icount),xparam1-x(:,icount),Verbose,Save_files);
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hh=inv(H);
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hhg=hh;
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else
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hh0 = reshape(dum,nx,nx);
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hh=hhg;
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if flagit==2
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if min(eig(hh0))<=0
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hh0=hhg; %generalized_cholesky(hh0);
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else
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hh=hh0;
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igg=inv(hh);
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end
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end
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H = igg;
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end
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elseif analytic_derivation
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[fvalx,exit_flag,gg,hh]=penalty_objective_function(xparam1,func0,penalty,varargin{:});
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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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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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g(:,icount+1)=gg;
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if Save_files
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save('m1.mat','x','hh','g','hhg','igg','fval0','nig','H')
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end
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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','nig')
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end
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if ftol>ftol0
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skipline()
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disp_verbose('Numerical noise in the likelihood',Verbose)
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disp_verbose('Tolerance had to be relaxed',Verbose)
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skipline()
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end
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if jit==nit
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skipline()
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disp_verbose('Maximum number of iterations reached',Verbose)
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skipline()
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end
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if norm(gg)<=gtol
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disp_verbose(['Estimation ended:'],Verbose)
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disp_verbose(['Gradient norm < ', num2str(gtol)],Verbose)
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end
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if check==1
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disp_verbose(['Estimation successful.'],Verbose)
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end
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return
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function x = check_bounds(x,bounds)
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inx = find(x>=bounds(:,2));
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if ~isempty(inx)
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x(inx) = bounds(inx,2)-eps;
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end
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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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