function [dq,rq]=fdim(q,x,trace);
% from fdim.sh
% Estimates generalised fractal dimensions of a set of points x;
% e.g. q=0 is Hausdorf,  q=1 is Information,  q=2 is Correlation,  etc.
% v0.20   1/7/94, copyright AJ Roberts, aroberts@usq.edu.au
% Made publically available under the GNU arrangements.
%
% x(j,:) = coordinates of the jth point of a set; % should be embeded;
%   q    = row vector of exponents
%  dq    = corresponding row of qth generalised dimension
%  rq    = optimistic range-factor over which the dim holds
% trace  = optional argument: set to 1 if you want trace prints and graphics
%          otherwise omit or set to 0
%
% The following parameters may be changed---at your own risk.
rrat=2;   % square of radius-ratio for covering disks.  
tol=0.03; % approx error in minimisation of curve fit.

if nargin<3, trace=0; end
[n,m]=size(x);
lrat=log(rrat);
rmax=sqrt(m)*max(max(x)-min(x));
lrrmax=2*log(rmax);
if trace, disp('computing distance histogram'); end;
t0=clock;
unwarn=1;
nor=[];
for j=1:n;
   rr= sum( [ zeros(n,1)  (x-ones(n,1)*x(j,:) ).^2 ]' );
   k=1+floor( (lrrmax-log(rr(rr>0)))/lrat );
   nor(j,max(k))=0;
   for l=k; nor(j,l)=nor(j,l)+1; end;
   if unwarn, et=etime(clock,t0);
      if (et>5)&(2*j<n),
         et=(n-j)*5/j;
         disp([num2str(et) 'secs to go']);
         unwarn=0;
      end;
   end;
end;
nor=cumsum([ones(1,n);flipud(nor')])'/n;
[j,nr]=size(nor);
lrat=lrat/2;
lrad=log(rmax)+((-nr+1):0)*lrat;
%
% fit the curves for each exponent q
% Ref: Pawelzik & Schuster, Phys Rev A 35 (1987) pp481--484.
lrad=[lrad(1)-lrat lrad lrad(nr)+lrat]'; % pad out
dq=[];
rq=[];
for qi=q,
%    if trace, disp(['analysing q = ' num2str(qi)]); end;
   if abs(qi-1)>sqrt(eps) , 
      lc=log( sum( nor.^(qi-1) )/n )/(qi-1);
   else 
      lc=sum( log(nor) )/n;
   end;
   j=find((lc<0.1*lc(1))&(lc>0.9*lc(1)));
   p=[lrad(min(j)) lrad(max(j)+2) 0.5 0.5];
%    p=fmins('rampdiff',p,[0 tol],[],lrad,[lc(1) lc 0]',trace);
   p=fminsearch('rampdiff',p,[],lrad,[lc(1) lc 0]',trace);
   di=(lc(nr)-lc(1))/(p(2)-p(1));
   dq=[dq di];
   rq=[rq p(2)-p(1)];
   if trace, 
      title(['q = ' num2str(qi) '  Dq = ' num2str(di)]); 
%       pause(1); 
   end
%    Dq(i)=dq;
end;
rq=exp(rq);
% end;
% END_OF_FILE
% if test 2107 -ne `wc -c <'fdim.m'`; then
%     echo shar: \"'fdim.m'\" unpacked with wrong size!
% fi
% # end of 'fdim.m'
% fi
% if test -f 'hint.m' -a "${1}" != "-c" ; then 
%   echo shar: Will not clobber existing file \"'hint.m'\"
% else
% echo shar: Extracting \"'hint.m'\" \(345 characters\)
% sed "s/^X//" >'hint.m' <<'END_OF_FILE'