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function [f0, x, ig] = mr_gstep(h1,x,bounds,func0,penalty,htol0,Verbose,Save_files,gradient_epsilon,parameter_names,robust,varargin)
% [f0, x, ig] = mr_gstep(h1,x,bounds,func0,penalty,htol0,Verbose,Save_files,gradient_epsilon,parameter_names,robust,varargin)
%
% Gibbs type step in optimisation
%
% varargin{1} --> dataset_
% varargin{2} --> dataset_info
% varargin{3} --> options_
% varargin{4} --> M_
% varargin{5} --> estim_params_
% varargin{6} --> bayestopt_
% varargin{7} --> BoundsInfo
% varargin{8} --> oo_
% Copyright © 2006-2023 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
n=size(x,1);
if isempty(h1)
h1=gradient_epsilon*ones(n,1);
end
if isempty(htol0)
htol = 1.e-6;
else
htol = htol0;
end
if length(htol)==1
htol=htol*ones(n,1);
end
f0=penalty_objective_function(x,func0,penalty,varargin{:});
xh1=x;
f1=zeros(size(f0,1),n);
f_1=f1;
i=0;
ig=zeros(n,1);
while i<n
i=i+1;
h10=h1(i);
hcheck=0;
dx=[];
xh1(i)=x(i)+h1(i);
fx = penalty_objective_function(xh1,func0,penalty,varargin{:});
f1(:,i)=fx;
xh1(i)=x(i)-h1(i);
fx = penalty_objective_function(xh1,func0,penalty,varargin{:});
f_1(:,i)=fx;
if hcheck && htol(i)<1
htol(i)=min(1,max(min(abs(dx))*2,htol(i)*10));
h1(i)=h10;
xh1(i)=x(i);
i=i-1;
else
gg=zeros(size(x));
hh=gg;
gg(i)=(f1(i)'-f_1(i)')./(2.*h1(i));
hh(i) = 1/max(1.e-9,abs( (f1(i)+f_1(i)-2*f0)./(h1(i)*h1(i)) ));
if gg(i)*(hh(i)*gg(i))/2 > htol(i)
[ff, xx,~,retcode] = csminit1(func0,x,penalty,f0,gg,0,diag(hh),Verbose,varargin{:});
if retcode && robust
if abs(x(i))<1.e-6
xa=transpose(linspace(x(i)/2, sign(x(i))*1.e-6*3/2, 7));
else
xa=transpose(linspace(x(i)/2, x(i)*3/2, 7));
end
fa=NaN(7,1);
for k=1:7
xh1(i)=xa(k);
fa(k,1) = penalty_objective_function(xh1,func0,penalty,varargin{:});
end
b=[ones(7,1) xa xa.*xa./2]\fa;
gg(i)=x(i)*b(3)+b(2);
hh(i)=1/b(3);
[ff2, xx2] = csminit1(func0,x,penalty,f0,gg,0,diag(hh),Verbose,varargin{:});
if ff2<ff
ff=ff2;
xx=xx2;
end
if min(fa)<ff
[ff, im]=min(fa);
xx(i)=xa(im);
end
end
ig(i)=1;
if robust
if not(isequal(xx , check_bounds(xx,bounds)))
xx = check_bounds(xx,bounds);
if xx(i)<x(i)
% lower bound
xx(i) = min(xx(i)+h1(i), 0.5*(xx(i)+x(i)));
else
% upper bound
xx(i) = max(xx(i)-h1(i), 0.5*(xx(i)+x(i)));
end
[ff,exit_flag]=penalty_objective_function(xx,func0,penalty,varargin{:});
if exit_flag~=1
disp_verbose('last step exited with bad status!',Verbose)
elseif ff<f0
f0=ff;
x=xx;
end
else
% check improvement wrt predicted one
if abs(f0-ff) < abs(gg(i)*(hh(i)*gg(i))/2/100) || abs(x(i)-xx(i))<1.e-10
[ff1, xx1] = csminit1(func0,x,penalty,f0,-gg,0,diag(hh),Verbose,varargin{:});
if not(isequal(xx1 , check_bounds(xx1,bounds)))
xx1 = check_bounds(xx1,bounds);
if xx1(i)<x(i)
% lower bound
xx1(i) = min(xx1(i)+h1(i), 0.5*(xx1(i)+x(i)));
else
% upper bound
xx1(i) = max(xx1(i)-h1(i), 0.5*(xx1(i)+x(i)));
end
[ff1,exit_flag]=penalty_objective_function(xx1,func0,penalty,varargin{:});
if exit_flag~=1
disp_verbose('last step exited with bad status!',Verbose)
end
end
if ff1<ff
ff=ff1;
xx=xx1;
end
end
f0=ff;
x=xx;
end
else
f0=ff;
x=xx;
x = check_bounds(x,bounds);
end
if Verbose
fprintf('Done for param %s = %8.4f; f = %8.4f\n',parameter_names{i},x(i),f0)
end
end
xh1=x;
end
if Save_files
save('gstep.mat','x','h1','f0')
end
end
if Save_files
save('gstep.mat','x','h1','f0')
end
return
function x = check_bounds(x,bounds)
inx = find(x>=bounds(:,2));
if ~isempty(inx)
x(inx) = bounds(inx,2)-1.e-10;
end
inx = find(x<=bounds(:,1));
if ~isempty(inx)
x(inx) = bounds(inx,1)+1.e-10;
end
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