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function [theta, fxsim, neval] = rotated_slice_sampler(objective_function,theta,thetaprior,sampler_options,varargin)
% ----------------------------------------------------------
% ROTATED SLICE SAMPLER - with stepping out (Neal, 2003)
% extension of the orthogonal univarite sampler (slice_sampler.m)
% copyright M. Ratto (European Commission)
%
% objective_function(theta,varargin): -log of any unnormalized pdf
% with varargin (optional) a vector of auxiliaty parameters
% to be passed to f( ).
% ----------------------------------------------------------
%
% INPUTS
% objective_function: objective function (expressed as minus the log of a density)
% theta: last value of theta
% thetaprior: bounds of the theta space
% sampler_options: posterior sampler options
% varargin: optional input arguments to objective function
%
% OUTPUTS
% theta: new theta sample
% fxsim: value of the objective function for the new sample
% neval: number of function evaluations
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2015-2017 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 <http://www.gnu.org/licenses/>.
theta=theta(:);
npar = length(theta);
neval = zeros(npar,1);
W1=[];
if isfield(sampler_options,'WR')
W1 = sampler_options.WR;
end
if ~isempty(sampler_options.mode)
mm = sampler_options.mode;
n = length(mm);
for j=1:n
distance(j)=sqrt(sum((theta-mm(j).m).^2));
end
[m, im] = min(distance);
r=im;
V1 = mm(r).m;
jj=0;
for j=1:n
if j~=r
jj=jj+1;
tmp=mm(j).m-mm(r).m;
%tmp=mm(j).m-theta;
V1(:,jj)=tmp/norm(tmp);
end
end
resul=randperm(n-1,n-1);
V1 = V1(:,resul);
%V1 = V1(:, randperm(n-1));
% %d = chol(mm(r).invhess);
% %V1 = transpose(feval(sampler_options.proposal_distribution, transpose(mm(r).m), d, npar));
%
% V1=eye(npar);
% V1=V1(:,randperm(npar));
% for j=1:2,
% V1(:,j)=mm(r(j)).m-theta;
% V1(:,j)=V1(:,j)/norm(V1(:,j));
% end
% % Gram-Schmidt
% for j=2:npar,
% for k=1:j-1,
% V1(:,j)=V1(:,j)-V1(:,k)'*V1(:,j)*V1(:,k);
% end
% V1(:,j)=V1(:,j)/norm(V1(:,j));
% end
% for j=1:n,
% distance(j)=sqrt(sum((theta-mm(j).m).^2));
% end
% [m, im] = min(distance);
% if im==r,
% fxsim=[];
% return,
% else
% theta1=theta;
% end
else
V1 = sampler_options.V1;
end
npar=size(V1,2);
for it=1:npar
theta0 = theta;
neval(it) = 0;
xold = 0;
% XLB = thetaprior(3);
% XUB = thetaprior(4);
tb=sort([(thetaprior(:,1)-theta)./V1(:,it) (thetaprior(:,2)-theta)./V1(:,it)],2);
XLB=max(tb(:,1));
XUB=min(tb(:,2));
if isempty(W1)
W = (XUB-XLB); %*0.8;
else
W = W1(it);
end
% -------------------------------------------------------
% 1. DRAW Z = ln[f(X0)] - EXP(1) where EXP(1)=-ln(U(0,1))
% THIS DEFINES THE SLICE S={x: z < ln(f(x))}
% -------------------------------------------------------
fxold = -feval(objective_function,theta,varargin{:});
%I have to be sure that the rotation is for L,R or for Fxold, theta(it)
neval(it) = neval(it) + 1;
Z = fxold + log(rand(1,1));
% -------------------------------------------------------------
% 2. FIND I=(L,R) AROUND X0 THAT CONTAINS S AS MUCH AS POSSIBLE
% STEPPING-OUT PROCEDURE
% -------------------------------------------------------------
u = rand(1,1);
L = max(XLB,xold-W*u);
R = min(XUB,L+W);
%[L R]=slice_rotation(L, R, alpha);
while(L > XLB)
xsim = L;
theta = theta0+xsim*V1(:,it);
fxl = -feval(objective_function,theta,varargin{:});
neval(it) = neval(it) + 1;
if (fxl <= Z)
break
end
L = max(XLB,L-W);
end
while(R < XUB)
xsim = R;
theta = theta0+xsim*V1(:,it);
fxr = -feval(objective_function,theta,varargin{:});
neval(it) = neval(it) + 1;
if (fxr <= Z)
break
end
R = min(XUB,R+W);
end
% ------------------------------------------------------
% 3. SAMPLING FROM THE SET A = (I INTERSECT S) = (LA,RA)
% ------------------------------------------------------
fxsim = Z-1;
while (fxsim < Z)
u = rand(1,1);
xsim = L + u*(R - L);
theta = theta0+xsim*V1(:,it);
fxsim = -feval(objective_function,theta,varargin{:});
neval(it) = neval(it) + 1;
if (xsim > xold)
R = xsim;
else
L = xsim;
end
end
end
% if ~isempty(sampler_options.mode),
% dist1=sqrt(sum((theta-mm(r).m).^2));
% if dist1>distance(r),
% theta=theta1;
% fxsim=[];
% end
% end
end
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