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function [fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,varargin)
% [fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,...
% P1,P2,P3,P4,P5,P6,P7,P8)
% retcodes: 0, normal step. 5, largest step still improves too fast.
% 4,2 back and forth adjustment of stepsize didn't finish. 3, smallest
% stepsize still improves too slow. 6, no improvement found. 1, zero
% gradient.
%---------------------
% Modified 7/22/96 to omit variable-length P list, for efficiency and compilation.
% Places where the number of P's need to be altered or the code could be returned to
% its old form are marked with ARGLIST comments.
%
% Fixed 7/17/93 to use inverse-hessian instead of hessian itself in bfgs
% update.
%
% Fixed 7/19/93 to flip eigenvalues of H to get better performance when
% it's not psd.
% NOTE: The display on screen can be turned off by seeting dispIndx=0 in this
% function. This option is used for the loop operation. T. Zha, 2 May 2000
%
% Copyright (C) 1997-2012 Christopher A. Sims
%
% This 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.
%
% It 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.
%
% If you did not received a copy of the GNU General Public License
% with this software, see <http://www.gnu.org/licenses/>.
%
dispIndx = 0; % 1: turn on all the diplays on the screen; 0: turn off (Added by T. Zha)
%
%tailstr = ')';
%for i=nargin-6:-1:1
% tailstr=[ ',P' num2str(i) tailstr];
%end
%ANGLE = .01; % when output of this variable becomes negative, we have wrong analytical graident
ANGLE = .005; % works for identified VARs and OLS
%THETA = .1; % works for OLS or other nonlinear functions
THETA = .3; %(0<THETA<.5) THETA near .5 makes long line searches, possibly fewer iterations.
% workds for identified VARs
FCHANGE = 1000;
MINLAMB = 1e-9;
% fixed 7/15/94
% MINDX = .0001;
% MINDX = 1e-6;
MINDFAC = .01;
fcount=0;
lambda=1;
xhat=x0;
f=f0;
fhat=f0;
g = g0;
gnorm = norm(g);
%
if (gnorm < 1.e-12) & ~badg % put ~badg 8/4/94
retcode =1;
dxnorm=0;
% gradient convergence
else
% with badg true, we don't try to match rate of improvement to directional
% derivative. We're satisfied just to get some improvement in f.
%
%if(badg)
% dx = -g*FCHANGE/(gnorm*gnorm);
% dxnorm = norm(dx);
% if dxnorm > 1e12
% disp('Bad, small gradient problem.')
% dx = dx*FCHANGE/dxnorm;
% end
%else
% Gauss-Newton step;
%---------- Start of 7/19/93 mod ---------------
%[v d] = eig(H0);
%toc
%d=max(1e-10,abs(diag(d)));
%d=abs(diag(d));
%dx = -(v.*(ones(size(v,1),1)*d'))*(v'*g);
% toc
dx = -H0*g;
% toc
dxnorm = norm(dx);
if dxnorm > 1e12
if dispIndx, disp('Near-singular H problem.'), end
dx = dx*FCHANGE/dxnorm;
end
dfhat = dx'*g0;
%end
%
%
if ~badg
% test for alignment of dx with gradient and fix if necessary
a = -dfhat/(gnorm*dxnorm);
if a<ANGLE
dx = dx - (ANGLE*dxnorm/gnorm+dfhat/(gnorm*gnorm))*g;
dfhat = dx'*g;
dxnorm = norm(dx);
if dispIndx, disp(sprintf('Correct for low angle: %g',a)), end
end
end
if dispIndx, disp(sprintf('Predicted improvement: %18.9f',-dfhat/2)), end
%
% Have OK dx, now adjust length of step (lambda) until min and
% max improvement rate criteria are met.
done=0;
factor=3;
shrink=1;
lambdaMin=0;
lambdaMax=inf;
lambdaPeak=0;
fPeak=f0;
lambdahat=0;
while ~done
if size(x0,2)>1
dxtest=x0+dx'*lambda;
else
dxtest=x0+dx*lambda;
end
% home
f = eval([fcn '(dxtest,varargin{:})']);
%ARGLIST
%f = feval(fcn,dxtest,P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11,P12,P13);
% f = feval(fcn,x0+dx*lambda,P1,P2,P3,P4,P5,P6,P7,P8);
if dispIndx, disp(sprintf('lambda = %10.5g; f = %20.7f',lambda,f )), end
%debug
%disp(sprintf('Improvement too great? f0-f: %g, criterion: %g',f0-f,-(1-THETA)*dfhat*lambda))
if f<fhat
fhat=f;
xhat=dxtest;
lambdahat = lambda;
end
fcount=fcount+1;
shrinkSignal = (~badg & (f0-f < max([-THETA*dfhat*lambda 0]))) | (badg & (f0-f) < 0) ;
growSignal = ~badg & ( (lambda > 0) & (f0-f > -(1-THETA)*dfhat*lambda) );
if shrinkSignal & ( (lambda>lambdaPeak) | (lambda<0) )
if (lambda>0) & ((~shrink) | (lambda/factor <= lambdaPeak))
shrink=1;
factor=factor^.6;
while lambda/factor <= lambdaPeak
factor=factor^.6;
end
%if (abs(lambda)*(factor-1)*dxnorm < MINDX) | (abs(lambda)*(factor-1) < MINLAMB)
if abs(factor-1) < MINDFAC
if abs(lambda)<4
retcode = 2;
else
retcode=7;
end
done=1;
end
end
if (lambda<lambdaMax) & (lambda>lambdaPeak)
lambdaMax=lambda;
end
lambda=lambda/factor;
if abs(lambda) < MINLAMB
if (lambda > 0) & (f0 <= fhat)
% try going against gradient, which may be inaccurate
lambda = -lambda*factor^6
else
if lambda < 0
retcode = 6;
else
retcode = 3;
end
done = 1;
end
end
elseif (growSignal & lambda>0) | (shrinkSignal & ((lambda <= lambdaPeak) & (lambda>0)))
if shrink
shrink=0;
factor = factor^.6;
%if ( abs(lambda)*(factor-1)*dxnorm< MINDX ) | ( abs(lambda)*(factor-1)< MINLAMB)
if abs(factor-1) < MINDFAC
if abs(lambda)<4
retcode = 4;
else
retcode=7;
end
done=1;
end
end
if ( f<fPeak ) & (lambda>0)
fPeak=f;
lambdaPeak=lambda;
if lambdaMax<=lambdaPeak
lambdaMax=lambdaPeak*factor*factor;
end
end
lambda=lambda*factor;
if abs(lambda) > 1e20;
retcode = 5;
done =1;
end
else
done=1;
if factor < 1.2
retcode=7;
else
retcode=0;
end
end
end
end
if dispIndx, disp(sprintf('Norm of dx %10.5g', dxnorm)), end
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