329 lines
12 KiB
Matlab
329 lines
12 KiB
Matlab
function [fh,xh,gh,H,itct,fcount,retcodeh] = csminwel1(fcn,x0,H0,grad,crit,nit,method,epsilon,Verbose,Save_files,varargin)
|
|
%[fhat,xhat,ghat,Hhat,itct,fcount,retcodeh] = csminwel1(fcn,x0,H0,grad,crit,nit,method,epsilon,varargin)
|
|
% Inputs:
|
|
% fcn: [string] string naming the objective function to be minimized
|
|
% x0: [npar by 1] initial value of the parameter vector
|
|
% H0: [npar by npar] initial value for the inverse Hessian. Must be positive definite.
|
|
% grad: [string or empty matrix] Either a string naming a function that calculates the gradient, or the null matrix.
|
|
% If it's null, the program calculates a numerical gradient. In this case fcn must
|
|
% be written so that it can take a matrix argument and produce a row vector of values.
|
|
% crit: [scalar] Convergence criterion. Iteration will cease when it proves impossible to improve the
|
|
% function value by more than crit.
|
|
% nit: [scalar] Maximum number of iterations.
|
|
% method: [scalar] integer scalar for selecting gradient method: 2, 3 or 5 points formula.
|
|
% epsilon: [scalar] scalar double, numerical differentiation increment
|
|
% varargin: Optional additional inputs that get handed off to fcn each
|
|
% time it is called.
|
|
%
|
|
% Note that if the program ends abnormally, it is possible to retrieve the current x,
|
|
% f, and H from the files g1.mat and H.mat that are written at each iteration and at each
|
|
% hessian update, respectively. (When the routine hits certain kinds of difficulty, it
|
|
% writes g2.mat and g3.mat as well. If all were written at about the same time, any of them
|
|
% may be a decent starting point. One can also start from the one with best function value.)
|
|
%
|
|
% Outputs:
|
|
% fh: [scalar] function value at minimum
|
|
% xh: [npar by 1] parameter vector at minimum
|
|
% gh [npar by 1] gradient vector
|
|
% H [npar by npar] inverse of the Hessian matrix
|
|
% itct [scalar] iteration count upon termination
|
|
% fcount [scalar] function iteration count upon termination
|
|
% retcodeh [scalar] return code:
|
|
% 0: normal step
|
|
% 1: zero gradient
|
|
% 2: back and forth on step length never finished
|
|
% 3: smallest step still improving too slow
|
|
% 4: back and forth on step length never finished
|
|
% 5: largest step still improving too fast
|
|
% 6: smallest step still improving too slow, reversed gradient
|
|
% 7: warning: possible inaccuracy in H matrix
|
|
%
|
|
% Original file downloaded from:
|
|
% http://sims.princeton.edu/yftp/optimize/mfiles/csminwel.m
|
|
%
|
|
% Copyright (C) 1993-2007 Christopher Sims
|
|
% Copyright (C) 2006-2015 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/>.
|
|
|
|
% initialize variable penalty
|
|
penalty = 1e8;
|
|
fh = [];
|
|
xh = [];
|
|
[nx,no]=size(x0);
|
|
nx=max(nx,no);
|
|
NumGrad= isempty(grad);
|
|
done=0;
|
|
itct=0;
|
|
fcount=0;
|
|
gh = [];
|
|
H = [];
|
|
retcodeh = [];
|
|
|
|
% force fcn, grad to function handle
|
|
if ischar(fcn)
|
|
fcn = str2func(fcn);
|
|
end
|
|
if ischar(grad)
|
|
grad = str2func(grad);
|
|
end
|
|
%tailstr = ')';
|
|
%stailstr = [];
|
|
% Lines below make the number of Pi's optional. This is inefficient, though, and precludes
|
|
% use of the matlab compiler. Without them, we use feval and the number of Pi's must be
|
|
% changed with the editor for each application. Places where this is required are marked
|
|
% with ARGLIST comments
|
|
%for i=nargin-6:-1:1
|
|
% tailstr=[ ',P' num2str(i) tailstr];
|
|
% stailstr=[' P' num2str(i) stailstr];
|
|
%end
|
|
|
|
[f0,cost_flag,arg1] = penalty_objective_function(x0,fcn,penalty,varargin{:});
|
|
|
|
if ~cost_flag
|
|
disp_verbose('Bad initial parameter.',Verbose)
|
|
return
|
|
end
|
|
|
|
if NumGrad
|
|
[g, badg]=get_num_grad(method,fcn,penalty,f0,x0,epsilon,varargin{:});
|
|
elseif ischar(grad)
|
|
[g,badg] = grad(x0,varargin{:});
|
|
else
|
|
g=arg1;
|
|
badg=0;
|
|
end
|
|
retcode3=101;
|
|
x=x0;
|
|
f=f0;
|
|
H=H0;
|
|
cliff=0;
|
|
while ~done
|
|
% penalty for dsge_likelihood and dsge_var_likelihood
|
|
penalty = f;
|
|
|
|
g1=[]; g2=[]; g3=[];
|
|
%addition fj. 7/6/94 for control
|
|
disp_verbose('-----------------',Verbose)
|
|
disp_verbose(sprintf('f at the beginning of new iteration, %20.10f',f),Verbose)
|
|
%-----------Comment out this line if the x vector is long----------------
|
|
% disp_verbose([sprintf('x = ') sprintf('%15.8g %15.8g %15.8g %15.8g\n',x)]);
|
|
%-------------------------
|
|
itct=itct+1;
|
|
[f1, x1, fc, retcode1] = csminit1(fcn,x,penalty,f,g,badg,H,Verbose,varargin{:});
|
|
fcount = fcount+fc;
|
|
% erased on 8/4/94
|
|
% if (retcode == 1) || (abs(f1-f) < crit)
|
|
% done=1;
|
|
% end
|
|
% if itct > nit
|
|
% done = 1;
|
|
% retcode = -retcode;
|
|
% end
|
|
if retcode1 ~= 1
|
|
if retcode1==2 || retcode1==4
|
|
wall1=1; badg1=1;
|
|
else
|
|
if NumGrad
|
|
[g1, badg1]=get_num_grad(method,fcn,penalty,f1,x1,epsilon,varargin{:});
|
|
elseif ischar(grad),
|
|
[g1, badg1] = grad(x1,varargin{:});
|
|
else
|
|
[junk1,cost_flag,g1] = penalty_objective_function(x1,fcn,penalty,varargin{:});
|
|
badg1 = ~cost_flag;
|
|
end
|
|
wall1=badg1;
|
|
% g1
|
|
if Save_files
|
|
save('g1.mat','g1','x1','f1','varargin');
|
|
end
|
|
end
|
|
if wall1 % && (~done) by Jinill
|
|
% Bad gradient or back and forth on step length. Possibly at
|
|
% cliff edge. Try perturbing search direction.
|
|
%
|
|
%fcliff=fh;xcliff=xh;
|
|
Hcliff=H+diag(diag(H).*rand(nx,1));
|
|
disp_verbose('Cliff. Perturbing search direction.',Verbose)
|
|
[f2, x2, fc, retcode2] = csminit1(fcn,x,penalty,f,g,badg,Hcliff,Verbose,varargin{:});
|
|
fcount = fcount+fc; % put by Jinill
|
|
if f2 < f
|
|
if retcode2==2 || retcode2==4
|
|
wall2=1; badg2=1;
|
|
else
|
|
if NumGrad
|
|
[g2, badg2]=get_num_grad(method,fcn,penalty,f2,x2,epsilon,varargin{:});
|
|
elseif ischar(grad),
|
|
[g2, badg2] = grad(x2,varargin{:});
|
|
else
|
|
[junk2,cost_flag,g2] = penalty_objective_function(x1,fcn,penalty,varargin{:});
|
|
badg2 = ~cost_flag;
|
|
end
|
|
wall2=badg2;
|
|
% g2
|
|
if Verbose
|
|
badg2
|
|
end
|
|
if Save_files
|
|
save('g2.mat','g2','x2','f2','varargin');
|
|
end
|
|
end
|
|
if wall2
|
|
disp_verbose('Cliff again. Try traversing',Verbose)
|
|
if norm(x2-x1) < 1e-13
|
|
f3=f; x3=x; badg3=1;retcode3=101;
|
|
else
|
|
gcliff=((f2-f1)/((norm(x2-x1))^2))*(x2-x1);
|
|
if(size(x0,2)>1)
|
|
gcliff=gcliff';
|
|
end
|
|
[f3, x3, fc, retcode3] = csminit1(fcn,x,penalty,f,gcliff,0,eye(nx),Verbose,varargin{:});
|
|
fcount = fcount+fc; % put by Jinill
|
|
if retcode3==2 || retcode3==4
|
|
wall3=1;
|
|
badg3=1;
|
|
else
|
|
if NumGrad
|
|
[g3, badg3]=get_num_grad(method,fcn,penalty,f3,x3,epsilon,varargin{:});
|
|
elseif ischar(grad),
|
|
[g3, badg3] = grad(x3,varargin{:});
|
|
else
|
|
[junk3,cost_flag,g3] = penalty_objective_function(x1,fcn,penalty,varargin{:});
|
|
badg3 = ~cost_flag;
|
|
end
|
|
wall3=badg3;
|
|
% g3
|
|
if Save_files
|
|
save('g3.mat','g3','x3','f3','varargin');
|
|
end
|
|
end
|
|
end
|
|
else
|
|
f3=f; x3=x; badg3=1; retcode3=101;
|
|
end
|
|
else
|
|
f3=f; x3=x; badg3=1;retcode3=101;
|
|
end
|
|
else
|
|
% normal iteration, no walls, or else we're finished here.
|
|
f2=f; f3=f; badg2=1; badg3=1; retcode2=101; retcode3=101;
|
|
end
|
|
else
|
|
f2=f;f3=f;f1=f;retcode2=retcode1;retcode3=retcode1;
|
|
end
|
|
%how to pick gh and xh
|
|
if f3 < f - crit && badg3==0 && f3 < f2 && f3 < f1
|
|
ih=3;
|
|
fh=f3;xh=x3;gh=g3;badgh=badg3;retcodeh=retcode3;
|
|
elseif f2 < f - crit && badg2==0 && f2 < f1
|
|
ih=2;
|
|
fh=f2;xh=x2;gh=g2;badgh=badg2;retcodeh=retcode2;
|
|
elseif f1 < f - crit && badg1==0
|
|
ih=1;
|
|
fh=f1;xh=x1;gh=g1;badgh=badg1;retcodeh=retcode1;
|
|
else
|
|
[fh,ih] = min([f1,f2,f3]);
|
|
%disp_verbose(sprintf('ih = %d',ih))
|
|
%eval(['xh=x' num2str(ih) ';'])
|
|
switch ih
|
|
case 1
|
|
xh=x1;
|
|
case 2
|
|
xh=x2;
|
|
case 3
|
|
xh=x3;
|
|
end %case
|
|
%eval(['gh=g' num2str(ih) ';'])
|
|
%eval(['retcodeh=retcode' num2str(ih) ';'])
|
|
retcodei=[retcode1,retcode2,retcode3];
|
|
retcodeh=retcodei(ih);
|
|
if exist('gh')
|
|
nogh=isempty(gh);
|
|
else
|
|
nogh=1;
|
|
end
|
|
if nogh
|
|
if NumGrad
|
|
[gh, badgh]=get_num_grad(method,fcn,penalty,fh,xh,epsilon,varargin{:});
|
|
elseif ischar(grad),
|
|
[gh, badgh] = grad(xh,varargin{:});
|
|
else
|
|
[junkh,cost_flag,gh] = penalty_objective_function(x1,fcn,penalty,varargin{:});
|
|
badgh = ~cost_flag;
|
|
end
|
|
end
|
|
badgh=1;
|
|
end
|
|
%end of picking
|
|
stuck = (abs(fh-f) < crit);
|
|
if (~badg) && (~badgh) && (~stuck)
|
|
H = bfgsi1(H,gh-g,xh-x,Verbose,Save_files);
|
|
end
|
|
disp_verbose('----',Verbose)
|
|
disp_verbose(sprintf('Improvement on iteration %d = %18.9f',itct,f-fh),Verbose)
|
|
% if Verbose
|
|
if itct > nit
|
|
disp_verbose('iteration count termination',Verbose)
|
|
done = 1;
|
|
elseif stuck
|
|
disp_verbose('improvement < crit termination',Verbose)
|
|
done = 1;
|
|
end
|
|
rc=retcodeh;
|
|
if Verbose || done
|
|
if rc ==0
|
|
%do nothing, just a normal step
|
|
elseif rc == 1
|
|
disp_verbose('zero gradient',Verbose)
|
|
elseif rc == 6
|
|
disp_verbose('smallest step still improving too slow, reversed gradient',Verbose)
|
|
elseif rc == 5
|
|
disp_verbose('largest step still improving too fast',Verbose)
|
|
elseif (rc == 4) || (rc==2)
|
|
disp_verbose('back and forth on step length never finished',Verbose)
|
|
elseif rc == 3
|
|
disp_verbose('smallest step still improving too slow',Verbose)
|
|
elseif rc == 7
|
|
disp_verbose('warning: possible inaccuracy in H matrix',Verbose)
|
|
else
|
|
error('Unaccounted Case, please contact the developers',Verbose)
|
|
end
|
|
end
|
|
|
|
f=fh;
|
|
x=xh;
|
|
g=gh;
|
|
badg=badgh;
|
|
end
|
|
|
|
end
|
|
|
|
function [g, badg]=get_num_grad(method,fcn,penalty,f0,x0,epsilon,varargin)
|
|
switch method
|
|
case 2
|
|
[g,badg] = numgrad2(fcn, f0, x0, penalty, epsilon, varargin{:});
|
|
case 3
|
|
[g,badg] = numgrad3(fcn, f0, x0, penalty, epsilon, varargin{:});
|
|
case 5
|
|
[g,badg] = numgrad5(fcn, f0, x0, penalty, epsilon, varargin{:});
|
|
case 13
|
|
[g,badg] = numgrad3_(fcn, f0, x0, penalty, epsilon, varargin{:});
|
|
case 15
|
|
[g,badg] = numgrad5_(fcn, f0, x0, penalty, epsilon, varargin{:});
|
|
otherwise
|
|
error('csminwel1: Unknown method for gradient evaluation!')
|
|
end
|
|
end |