fracscalexp.m

基于小波变换的分形学

function tau = FracScalExp(z,scale,loscale)
% FracScalExp -- Calculate Moment Generating Function
%  Usage
%    tau = FracScalExp(z,a,loscale,hiscale)
%  Inputs
%    z         matrix nexp by nscale of z(q,a) ``Thermo Partition Func''
%    scale         list of scales 
%    loscale   optional min scale to fit line by
%  Outputs
%    tau       vector 1 by nscale of moments
%
%  Description
%    tau(q) = Slope [ log(z(q,a))  versus log(a) ]
%	section 6.5.2 of Mallat's book
%
%  See Also
%    FracPartition
%

	if nargin < 3,
		loscale = 0.;
		hiscale = 10^32;
	end
	
	
	[nq,nscale]     = size(z);
	tau = zeros(nq,1);
	if nscale ~= size(scale),
		disp('FracScalExp: no match between z and a')
	end
	
	window = (loscale <= scale) & (scale <= hiscale);
	ix     = find(window);
	l = length(ix);
	if length(ix)>1,
		for kq =1:nq,
		 	y       =  log(z(kq,ix));   
			x = x-mean(x);			
			tau(kq) = sum(y.*x) / sum(x.*x);
%			tau(kq) = (y(l)-y(1)) ./ (x(l)-x(1));
%			tau(kq) = sum(y./x)./l;
		end
	else
		disp('FracScalExp: not enough data to determine slope')
	end