function [xparam1, hh, gg, fval, igg] = newrat(func0, x, analytic_derivation, ftol0, nit, flagg, DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
%  [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, varargin)
%
%  Optimiser with outer product gradient and with sequences of univariate steps
%  uses Chris Sims subroutine for line search
%
%  func0 = name of the function
%  there must be a version of the function called [func0,'_hh.m'], that also
%  gives as second OUTPUT the single contributions at times t=1,...,T
%    of the log-likelihood to compute outer product gradient
%
%  x = starting guess
%  analytic_derivation = 1 if analytic derivs
%  ftol0 = ending criterion for function change
%  nit = maximum number of iterations
%
%  In each iteration, Hessian is computed with outer product gradient.
%  for final Hessian (to start Metropolis):
%  flagg = 0, final Hessian computed with outer product gradient
%  flagg = 1, final 'mixed' Hessian: diagonal elements computed with numerical second order derivatives
%             with correlation structure as from outer product gradient,
%  flagg = 2, full numerical Hessian
%
%  varargin = list of parameters for func0

% Copyright (C) 2004-2013 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/>.

global objective_function_penalty_base

icount=0;
nx=length(x);
xparam1=x;
%ftol0=1.e-6;
htol_base = max(1.e-7, ftol0);
flagit=0;  % mode of computation of hessian in each iteration
ftol=ftol0;
gtol=1.e-3;
htol=htol_base;
htol0=htol_base;
gibbstol=length(BayesInfo.pshape)/50; %25;

% func0 = str2func([func2str(func0),'_hh']);
% func0 = func0;
[fval0,gg,hh]=feval(func0,x,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
fval=fval0;

% initialize mr_gstep and mr_hessian

outer_product_gradient=1;
if isempty(hh)
    mr_hessian(1,x,[],[],[],DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
    [dum, gg, htol0, igg, hhg, h1]=mr_hessian(0,x,func0,flagit,htol,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
    if isempty(dum),
        outer_product_gradient=0;
        igg = 1e-4*eye(nx);
    else
        hh0 = reshape(dum,nx,nx);
        hh=hhg;
        if min(eig(hh0))<0
            hh0=hhg; %generalized_cholesky(hh0);
        elseif flagit==2
            hh=hh0;
            igg=inv(hh);
        end
    end
    if htol0>htol
        htol=htol0;
    end
else
    hh0=hh;
    hhg=hh;
    igg=inv(hh);
    h1=[];
end
H = igg;
disp(['Gradient norm ',num2str(norm(gg))])
ee=eig(hh);
disp(['Minimum Hessian eigenvalue ',num2str(min(ee))])
disp(['Maximum Hessian eigenvalue ',num2str(max(ee))])
g=gg;
check=0;
if max(eig(hh))<0, disp('Negative definite Hessian! Local maximum!'), pause, end,
save m1.mat x hh g hhg igg fval0

igrad=1;
igibbs=1;
inx=eye(nx);
jit=0;
nig=[];
ig=ones(nx,1);
ggx=zeros(nx,1);
while norm(gg)>gtol && check==0 && jit<nit
    jit=jit+1;
    tic
    icount=icount+1;
    objective_function_penalty_base = fval0(icount);
    disp([' '])
    disp(['Iteration ',num2str(icount)])
    [fval,x0,fc,retcode] = csminit1(func0,xparam1,fval0(icount),gg,0,H,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
    if igrad
        [fval1,x01,fc,retcode1] = csminit1(func0,x0,fval,gg,0,inx,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
        if (fval-fval1)>1
            disp('Gradient step!!')
        else
            igrad=0;
        end
        fval=fval1;
        x0=x01;
    end
    if icount==1 || (icount>1 && (fval0(icount-1)-fval0(icount))>1) || ((fval0(icount)-fval)<1.e-2*(gg'*(H*gg))/2 && igibbs),
        if length(find(ig))<nx
            ggx=ggx*0;
            ggx(find(ig))=gg(find(ig));
            if analytic_derivation,
                hhx=hh;
            else
                hhx = reshape(dum,nx,nx);
            end
            iggx=eye(length(gg));
            iggx(find(ig),find(ig)) = inv( hhx(find(ig),find(ig)) );
            [fvala,x0,fc,retcode] = csminit1(func0,x0,fval,ggx,0,iggx,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
        end
        [fvala, x0, ig] = mr_gstep(h1,x0,func0,htol,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
        nig=[nig ig];
        disp('Sequence of univariate steps!!')
        fval=fvala;
    end
    if (fval0(icount)-fval)<ftol && flagit==0
        disp('Try diagonal Hessian')
        ihh=diag(1./(diag(hhg)));
        [fval2,x0,fc,retcode2] = csminit1(func0,x0,fval,gg,0,ihh,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
        if (fval-fval2)>=ftol
            disp('Diagonal Hessian successful')
        end
        fval=fval2;
    end
    if (fval0(icount)-fval)<ftol && flagit==0
        disp('Try gradient direction')
        ihh0=inx.*1.e-4;
        [fval3,x0,fc,retcode3] = csminit1(func0,x0,fval,gg,0,ihh0,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
        if (fval-fval3)>=ftol
            disp('Gradient direction successful')
        end
        fval=fval3;
    end
    xparam1=x0;
    x(:,icount+1)=xparam1;
    fval0(icount+1)=fval;
    if (fval0(icount)-fval)<ftol
        disp('No further improvement is possible!')
        check=1;
        if analytic_derivation,
            [fvalx,gg,hh]=feval(func0,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
            hhg=hh;
            H = inv(hh);            
        else
        if flagit==2
            hh=hh0;
        elseif flagg>0
            [dum, gg, htol0, igg, hhg,h1]=mr_hessian(0,xparam1,func0,flagg,ftol0,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
            if flagg==2
                hh = reshape(dum,nx,nx);
                ee=eig(hh);
                if min(ee)<0
                    hh=hhg;
                end
            else
                hh=hhg;
            end
        end
        end
        disp(['Actual dxnorm ',num2str(norm(x(:,end)-x(:,end-1)))])
        disp(['FVAL          ',num2str(fval)])
        disp(['Improvement   ',num2str(fval0(icount)-fval)])
        disp(['Ftol          ',num2str(ftol)])
        disp(['Htol          ',num2str(htol0)])
        disp(['Gradient norm  ',num2str(norm(gg))])
        ee=eig(hh);
        disp(['Minimum Hessian eigenvalue ',num2str(min(ee))])
        disp(['Maximum Hessian eigenvalue ',num2str(max(ee))])
        g(:,icount+1)=gg;
    else
        df = fval0(icount)-fval;
        disp(['Actual dxnorm ',num2str(norm(x(:,end)-x(:,end-1)))])
        disp(['FVAL          ',num2str(fval)])
        disp(['Improvement   ',num2str(df)])
        disp(['Ftol          ',num2str(ftol)])
        disp(['Htol          ',num2str(htol0)])
        htol=htol_base;
        if norm(x(:,icount)-xparam1)>1.e-12 && analytic_derivation==0,
            try
                save m1.mat x fval0 nig -append
            catch
                save m1.mat x fval0 nig
            end
            [dum, gg, htol0, igg, hhg, h1]=mr_hessian(0,xparam1,func0,flagit,htol,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
            if isempty(dum),
                outer_product_gradient=0;
            end
            if htol0>htol
                htol=htol0;
                skipline()
                disp('Numerical noise in the likelihood')
                disp('Tolerance has to be relaxed')
                skipline()
            end
            if ~outer_product_gradient,
                H = bfgsi1(H,gg-g(:,icount),xparam1-x(:,icount));
                hh=inv(H);
                hhg=hh;
            else
                hh0 = reshape(dum,nx,nx);
                hh=hhg;
                if flagit==2
                    if min(eig(hh0))<=0
                        hh0=hhg; %generalized_cholesky(hh0);
                    else
                        hh=hh0;
                        igg=inv(hh);
                    end
                end
                H = igg;
            end
        elseif analytic_derivation,
            [fvalx,gg,hh]=feval(func0,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
            hhg=hh;
            H = inv(hh);
        end
        disp(['Gradient norm  ',num2str(norm(gg))])
        ee=eig(hh);
        disp(['Minimum Hessian eigenvalue ',num2str(min(ee))])
        disp(['Maximum Hessian eigenvalue ',num2str(max(ee))])
        if max(eig(hh))<0, disp('Negative definite Hessian! Local maximum!'), pause(1), end,
        t=toc;
        disp(['Elapsed time for iteration ',num2str(t),' s.'])
        g(:,icount+1)=gg;

        save m1.mat x hh g hhg igg fval0 nig H
    end
end

save m1.mat x hh g hhg igg fval0 nig
if ftol>ftol0
    skipline()
    disp('Numerical noise in the likelihood')
    disp('Tolerance had to be relaxed')
    skipline()
end

if jit==nit
    skipline()
    disp('Maximum number of iterations reached')
    skipline()
end

if norm(gg)<=gtol
    disp(['Estimation ended:'])
    disp(['Gradient norm < ', num2str(gtol)])
end
if check==1,
    disp(['Estimation successful.'])
end

return