MF－DFA.rar_DFA_MF-DFA matlab_MF-MDF_多重分形

clear all close all clc pvc1= dlmread('cu-01.txt','\t',[5000,1,8000,1]); %100(male 69) 正常 X = [pvc1]; x = 1:3001 plot(x,X); q = [-30:1:-8,-7.2:0.9:-5.4,-5.3:0.4:-2.9,-2.76:0.08:-0.2,-0.1:0.2:1,1.6:0.8:7.2,8:1:30]; % q = [-10:2:10]; % averageX=mean(X); % N=length(X); S = 4:10:500; % for i=1:N %%%%%%%%%%%%%%%%MF-DFA 算法的第一步，构造去均值的和序列 %for i2 = 1:size(X,2); %%size(X,2)返回X第二维的长度 N=length(X); averageX=sum(X)./N; Y = []; for a=1:N temp=0; for k=1:a temp=temp+(X(k)-averageX); end Y(a)=temp; end %%%%%%%%%%%%%%%%%第二次求离差 averageY = mean(Y); Y_1 = []; for a_1 = 1:N temp_1 = 0; for k_1 = 1:a_1 temp_1 = temp_1+(Y(k_1)-averageY); end Y_1(a_1)=temp_1; end M=length(Y_1); for q_i = 1:length(q) for i = 1:length(S) N1=floor(M/S(i)); y1 = reshape(Y_1(1:S(i)*N1),S(i),N1); %以下实现从前到后，从后到前划分序列，得S行，2*N1列 y2 = reshape(Y_1(M:-1:M-S(i)*N1+1),S(i),N1); y = [y1,y2]; N_totle = 2*N1; coefPoly = zeros(2,N_totle); %设置空数组为拟合做准备 valueFit = zeros(size(y)); for segment_ii = 1:N_totle %对划分后的每一个区间进行拟合 coefPoly(:,segment_ii) = polyfit([1:S(i)]',y(:,segment_ii),1); %分别去每一段进行拟合 valueFit(:,segment_ii) = polyval(coefPoly(:,segment_ii),1:S(i)); end diffMatrix = valueFit - y; %都是矩阵形式，得到多个数据 diffMMSE = mean(diffMatrix.^2); FuncQs(i) = (mean(diffMMSE.^(q(q_i)/2)))^(1/q(q_i)); %获得q阶波动函数Fq（s） end %figure(1),plot(log10(S),log10(FuncQs),'-ok','MarkerSize',8), xlabel('lgS'),ylabel('lgFq(S)');hold on coef = polyfit(log10(S),log10(FuncQs),1); valuepoly = polyval(coef,log10(S)); %figure(2),plot(log10(S),valuepoly,'-ok','MarkerSize',4), xlabel('lgS'),ylabel('valuepoly');hold on hq(q_i) = coef(1);%figure(1),plot(q(q_i),hq(q_i),'-ok','MarkerSize',4), xlabel('q'),ylabel('hq');hold on end figure(1),plot(q,hq,'-ok','MarkerSize',4), xlabel('q'),ylabel('hq');hold on %%%%%%%%%%%%%%%%%%%%求T(q)-q的关系图 T = []; for q_m = 1:length(q) T(q_m) = q(q_m).*hq(q_m)-1; end %figure(2),plot(q,T,'-ok','MarkerSize',4), xlabel('q'),ylabel('T(q)');hold on figure(2),plot(q,T,'-ok','MarkerSize',4), xlabel('q'),ylabel('T(q)');hold on %%%%%%%%%%%%%%%%%%%%%%%%%求多重分形谱 Dhq = diff(hq)./diff(q); alpha = [];f_alpha = []; for i = 1:length(Dhq) alpha(i) = hq(i) + q(i).* Dhq(i); f_alpha(i) = (q(i).^2).* Dhq(i) + 1; % F_alpha = abs(f_alpha); end %%%%%%%%%%%%%%%%%%%%%%%%%%%去掉f(a)中的负值 Alpha=[];F_alpha=[]; j=1; for i=1:length(f_alpha) if f_alpha(i)>0 F_alpha(j) = f_alpha(i); Alpha(j)=alpha(i); j=j+1; end end %figure(3),plot(Alpha,F_alpha,'-ok','MarkerSize',4), xlabel('Alpha'),ylabel('F_alpha');hold on figure(3),plot(Alpha,F_alpha,'-ok','MarkerSize',4),xlabel('Alpha'),ylabel('F_alpha');hold on % DFA=[];s=1; % DFA(s)=max(Alpha)-min(Alpha);s=s+1; % DFA(s)=max(F);