absval.m

分形分析中很重要的Hurst指数的计算程序,并包含Hurst指数等于0.7和0.8的两个样本序列

function H = absval(sequence,isplot,moment)
%
% 'absval' estimate the hurst parameter of a given sequence with absolute
%     moment method.
%
% Inputs:
%     sequence: the input sequence for estimate
%     isplot: whether display the plot. without a plot if isplot equal to 0
%     moment: a positive interger which used to calculate absolute moment     
% Outputs:
%     H: the estimated hurst coeffeient of the input sequence

%  Author: Chu Chen 
%  Version 1.0,  03/10/2008
%  [e-mail]
%

if nargin == 1
    moment = 1;
    isplot = 0;
end

if nargin == 2
    moment = 1;
end

sequence = sequence - mean(sequence);
N = length(sequence);
mlarge = floor(N/5); 
M = [floor(logspace(0,log10(mlarge),50))];
M = unique(M(M>1));
n = length(M);
cut_min = ceil(n/10);
cut_max = floor(6*n/10);

A = zeros(1,n);
for i = 1:n
    m = M(i);
    k = floor(N/m);
    matrix_sequence = reshape(sequence(1:m*k),m,k);    
    A(i) = sum((abs(mean(matrix_sequence))).^moment)/k;
end

x = log10(M);
y = log10(A);
y1 = -x + y(1) + x(1);
X = x(cut_min:cut_max);
Y = y(cut_min:cut_max);

p1 = polyfit(X,Y,1);
Yfit = polyval(p1,X);
yfit = polyval(p1,x);
alpha = (Yfit(end)-Yfit(1))/(X(end)-X(1));
H = 1+alpha/moment;

if isplot ~= 0
    figure,hold on;
    plot(x,y,'b*');
    plot(x,y1);
    plot(X,Yfit,'r-','LineWidth',2);
    plot(x(1:cut_min),yfit(1:cut_min),'r:','LineWidth',2);
    plot(x(cut_max:end),yfit(cut_max:end),'r:','LineWidth',2);
    xlabel('Log of Aggreate Level'), ylabel('Log of Absolute Moment'), title('Absolute Moment Method');
end