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v3+4: mr_hessian.m corrected by M. Ratto 

git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@592 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
michel 2006-01-09 15:53:39 +00:00
parent c642044b39
commit e62b80c658
1 changed files with 185 additions and 47 deletions
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232
matlab/mr_hessian.m
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@ -1,33 +1,68 @@
% Copyright (C) 2001 Michel Juillard
% Copyright (C) 2004 Marco Ratto
% adapted from Michel Juillard original rutine hessian.m
%
% computes second order partial derivatives
% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884
% [hessian_mat, gg, htol1, ihh, hh_mat0] = mr_hessian(func,x,hflag,htol0,varargin)
%
% Adapted by M. Ratto from original M. Juillard routine
% numerical gradient and Hessian, with 'automatic' check of numerical
% error
%
% func = name of the function: func must give two outputs:
% - the log-likelihood AND the single contributions at times t=1,...,T
% of the log-likelihood to compute outer product gradient
% x = parameter values
% hflag = 0, Hessian computed with outer product gradient, one point
% increments for partial derivatives in gradients
% hflag = 1, 'mixed' Hessian: diagonal elements computed with numerical second order derivatives
% with correlation structure as from outer product gradient;
% two point evaluation of derivatives for partial derivatives
% in gradients
% hflag = 2, full numerical Hessian, computes second order partial derivatives
% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27
% p. 884.
% htol0 = 'precision' of increment of function values for numerical
% derivatives
%
% varargin: other parameters of func
%
function [hessian_mat, gg] = mr_hessian(func,x,hflag,varargin)
global gstep_
persistent h1
function [hessian_mat, gg, htol1, ihh, hh_mat0] = mr_hessian(func,x,hflag,htol0,varargin)
global gstep_ bayestopt_
persistent h1 htol
if isempty(htol), htol = 1.e-4; end
func = str2func(func);
f0=feval(func,x,varargin{:});
[f0, ff0]=feval(func,x,varargin{:});
n=size(x,1);
h2=bayestopt_.ub-bayestopt_.lb;
%h1=max(abs(x),gstep_*ones(n,1))*eps^(1/3);
%h1=max(abs(x),sqrt(gstep_)*ones(n,1))*eps^(1/6);
if isempty(h1),
h1=max(abs(x),sqrt(gstep_)*ones(n,1))*eps^(1/4);
end
htol = 1.e-4;
if htol0<htol,
htol=htol0;
end
xh1=x;
f1=zeros(size(f0,1),n);
f_1=f1;
ff1=zeros(size(ff0));
ff_1=ff1;
for i=1:n,
%for i=1:n,
i=0;
while i<n,
i=i+1;
h10=h1(i);
hcheck=0;
dx=[];
xh1(i)=x(i)+h1(i);
fx=feval(func,xh1,varargin{:});
if abs(fx-f0)<htol | abs(fx-f0)>(5*htol),
[fx, ffx]=feval(func,xh1,varargin{:});
it=1;
dx=(fx-f0);
ic=0;
if abs(dx)>(2*htol),
c=mr_nlincon(xh1,varargin{:});
ic=0;
while c
h1(i)=h1(i)*0.9;
xh1(i)=x(i)+h1(i);
@ -35,53 +70,111 @@ for i=1:n,
ic=1;
end
if ic,
fx=feval(func,xh1,varargin{:});
[fx, ffx]=feval(func,xh1,varargin{:});
dx=(fx-f0);
end
icount = 0;
while abs(fx-f0)<htol & icount< 10,
icount=icount+1;
h1(i)=min(0.3*abs(x(i)), 1.e-3/(abs(fx-f0)/h1(i)));
end
icount = 0;
h0=h1(i);
while (abs(dx(it))<0.5*htol | abs(dx(it))>(2*htol)) & icount<10 & ic==0,
%while abs(dx(it))<0.5*htol & icount< 10 & ic==0,
icount=icount+1;
%if abs(dx(it)) ~= 0,
if abs(dx(it))<0.5*htol
if abs(dx(it)) ~= 0,
h1(i)=min(0.3*abs(x(i)), 0.9*htol/abs(dx(it))*h1(i));
else
h1(i)=2.1*h1(i);
end
xh1(i)=x(i)+h1(i);
c=mr_nlincon(xh1,varargin{:});
while c
h1(i)=h1(i)*0.9;
xh1(i)=x(i)+h1(i);
c=mr_nlincon(xh1,varargin{:});
end
fx=feval(func,xh1,varargin{:});
ic=1;
end
[fx, ffx]=feval(func,xh1,varargin{:});
end
while abs(fx-f0)>(5*htol),
h1(i)=h1(i)*0.5;
if abs(dx(it))>(2*htol),
h1(i)= htol/abs(dx(it))*h1(i);
xh1(i)=x(i)+h1(i);
fx=feval(func,xh1,varargin{:});
[fx, ffx]=feval(func,xh1,varargin{:});
while (fx-f0)==0,
h1(i)= h1(i)*2;
xh1(i)=x(i)+h1(i);
[fx, ffx]=feval(func,xh1,varargin{:});
ic=1;
end
end
it=it+1;
dx(it)=(fx-f0);
h0(it)=h1(i);
if h1(i)<1.e-12*min(1,h2(i)),
ic=1;
hcheck=1;
end
%else
% h1(i)=1;
% ic=1;
%end
end
% if (it>2 & dx(1)<10^(log10(htol)/2)) ,
% [dum, is]=sort(h0);
% if find(diff(sign(diff(dx(is)))));
% hcheck=1;
% end
% elseif (it>3 & dx(1)>10^(log10(htol)/2)) ,
% [dum, is]=sort(h0);
% if find(diff(sign(diff(dx(is(1:end-1))))));
% hcheck=1;
% end
% end
f1(:,i)=fx;
xh1(i)=x(i)-h1(i);
c=mr_nlincon(xh1,varargin{:});
ic=0;
while c
h1(i)=h1(i)*0.9;
ff1=ffx;
if hflag, % two point based derivatives
xh1(i)=x(i)-h1(i);
c=mr_nlincon(xh1,varargin{:});
ic = 1;
end
fx=feval(func,xh1,varargin{:});
f_1(:,i)=fx;
if ic,
xh1(i)=x(i)+h1(i);
f1(:,i)=feval(func,xh1,varargin{:});
c=mr_nlincon(xh1,varargin{:});
ic=0;
while c
h1(i)=h1(i)*0.9;
xh1(i)=x(i)-h1(i);
c=mr_nlincon(xh1,varargin{:});
ic = 1;
end
[fx, ffx]=feval(func,xh1,varargin{:});
f_1(:,i)=fx;
ff_1=ffx;
if ic,
xh1(i)=x(i)+h1(i);
[f1(:,i), ff1]=feval(func,xh1,varargin{:});
end
ggh(:,i)=(ff1-ff_1)./(2.*h1(i));
else
ggh(:,i)=(ff1-ff0)./h1(i);
end
xh1(i)=x(i);
if hcheck & htol<1,
htol=min(1,max(min(abs(dx))*2,htol*10));
h1(i)=h10;
i=0;
end
save hess
end
h_1=h1;
xh1=x;
xh_1=xh1;
gg=(f1'-f_1')./(2.*h1);
if hflag,
gg=(f1'-f_1')./(2.*h1);
else
gg=(f1'-f0)./h1;
end
if hflag==2,
gg=(f1'-f_1')./(2.*h1);
hessian_mat = zeros(size(f0,1),n*n);
for i=1:n
if i > 1
@ -96,35 +189,80 @@ if hflag,
xh_1(i)=x(i)-h1(i);
xh_1(j)=x(j)-h_1(j);
%hessian_mat(:,(i-1)*n+j)=-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j));
temp1 = feval(func,xh1,varargin{:});
%c=mr_nlincon(xh1,varargin{:});
%if c, disp( ['hessian warning cross ', num2str(c) ]), end
%temp1 = feval(func,xh1,varargin{:});
c=mr_nlincon(xh1,varargin{:});
lam=1;
while c,
lam=lam*0.9;
xh1(i)=x(i)+h1(i)*lam;
xh1(j)=x(j)+h_1(j)*lam;
%disp( ['hessian warning cross ', num2str(c) ]),
c=mr_nlincon(xh1,varargin{:});
end
temp1 = f0+(feval(func,xh1,varargin{:})-f0)/lam;
%temp2 = feval(func,xh_1,varargin{:});
c=mr_nlincon(xh_1,varargin{:});
while c,
lam=lam*0.9;
xh_1(i)=x(i)-h1(i)*lam;
xh_1(j)=x(j)-h_1(j)*lam;
%disp( ['hessian warning cross ', num2str(c) ]),
c=mr_nlincon(xh_1,varargin{:});
end
temp2 = f0+(feval(func,xh_1,varargin{:})-f0)/lam;
temp2 = feval(func,xh_1,varargin{:});
%c=mr_nlincon(xh_1,varargin{:});
%if c, disp( ['hessian warning cross ', num2str(c) ]), end
hessian_mat(:,(i-1)*n+j)=-(-temp1 -temp2+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j));
xh1(i)=x(i);
xh1(j)=x(j);
xh_1(i)=x(i);
xh_1(j)=x(j);
j=j+1;
save hess
end
i=i+1;
end
else
elseif hflag==1,
hessian_mat = zeros(size(f0,1),n*n);
for i=1:n,
dum = (f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i));
if dum>0,
if dum>eps,
hessian_mat(:,(i-1)*n+i)=dum;
else
hessian_mat(:,(i-1)*n+i)=gg(i)^2;
hessian_mat(:,(i-1)*n+i)=max(eps, gg(i)^2);
end
end
%hessian_mat2=hh_mat(:)';
end
gga=ggh.*kron(ones(size(ff1)),2.*h1'); % re-scaled gradient
hh_mat=gga'*gga; % rescaled outer product hessian
hh_mat0=ggh'*ggh; % outer product hessian
A=diag(2.*h1); % rescaling matrix
if hflag>0 & min(eig(reshape(hessian_mat,n,n)))>0,
hh0 = A*reshape(hessian_mat,n,n)*A'; %rescaled second order derivatives
sd0=sqrt(diag(hh0)); %rescaled 'standard errors' using second order derivatives
sd=sqrt(diag(hh_mat)); %rescaled 'standard errors' using outer product
hh_mat=hh_mat./(sd*sd').*(sd0*sd0'); %rescaled outer product with 'true' std's
hh0 = reshape(hessian_mat,n,n); % second order derivatives
sd0=sqrt(diag(hh0)); % 'standard errors' using second order derivatives
sd=sqrt(diag(hh_mat0)); % 'standard errors' using outer product
hh_mat0=hh_mat0./(sd*sd').*(sd0*sd0'); % rescaled outer product with 'true' std's
end
igg=inv(hh_mat); % inverted rescaled outer product hessian
ihh=A'*igg*A; % inverted outer product hessian
if hflag==0,
hessian_mat=hh_mat0(:);
end
if isnan(hessian_mat),
hh_mat0=eye(length(hh_mat0));
ihh=hh_mat0;
hessian_mat=hh_mat0(:);
end
hh1=h1;
htol1=htol;
save hess
% 11/25/03 SA Created from Hessian_sparse (removed sparse)