gp_algorithm.m

本文是通过文中方法来求最小嵌入维程序.子程序,相重构程序.

function D=GP_Algorithm(data,tau,max_m)
% GP算法求关联维和嵌入维
%clc
%---------------------------------------------------
x=data;
X = normalize_1(x);

%---------------------------------------------------'

disp('----- GP算法求关联维和嵌入维 -----');

% t = 1;
m_vector = 1:max_m;
r_vector = exp(-5:0.25:1);

num_m = length(m_vector);
num_r = length(r_vector);
ln_Cr = zeros(num_m,num_r);

%------------------------------------------------------
% tic
type_norm = 2;       % 使用范数类型 (缺省值为2)
                    % type_norm = 0,1,2时，分别对应无穷范数、1范数和2范数
block = 1;           % 分块计计算关联积分 - 分块数 (缺省值为1)
                    % t越大速度越快，但有误差
for i = 1:num_m
    i
    for j = 1:num_r
        % 计算关联积分S(m,N,r,t), 参见 <<混沌时间序列分析及应用>> P35 式(2.29)
        m = m_vector(i);
        r = r_vector(j);
        %ln_Cr(i,j) = log(CorrelationIntegral(m,X,r,t)); % 缺省用法
        ln_Cr(i,j) = log(CorrelationIntegral(m,X,r,tau,type_norm,block)); 
    end
end
% t = toc
subplot(211)
ln_r = log(r_vector);
plot(ln_r,ln_Cr','+:');grid;
xlabel('ln(r)'); ylabel('ln(C(r))');
title(['norm = ',num2str(type_norm),', block = ',num2str(block),', t = ',num2str(tau)]);
legend('m=2','m=3','m=4','m=5',4)
subplot(212)
 %------------------------------------------------------
    % 拟合线性区域
for i=1:num_m
   A=find(ln_Cr(i,:)~=-inf);
   t=A(1);
    LinearZone = [t:t+7];
    F = polyfit(ln_r(LinearZone),ln_Cr(i,LinearZone),1);
    D(i) = F(1);
end
 plot(D,'+:'); grid;