MATLAB指數(shù)擬合程序

(1)預(yù)處理數(shù)據(jù)為Iny=lna+b*x(2)用polyfit進行多項式擬合例如x=[1971:1990];y=[8.52298.71778.92219.08599.24209.37179.49749.62599.75429.870510.007210.165410.300810.435710.585110.750710.930011.102611.270411.4333];用上面的指數(shù)函數(shù)進行擬合程序如下：%%%%%%% x=[1971:1990];y=[8.52298.71778.92219.08599.24209.37179.49749.62599.75429.870510.007210.165410.300810.435710.585110.750710.930011.102611.270411.4333];Iog_y=Iog(y);P=polyfit(x,log_y,1);logy1=P(1)*x+P(2);y1=exp(logy1);plot(x,y,x,y1,'*')%%%%%%% 結(jié)果如下11.51.2包含非其次項擬合模型為：y=a1+a2*exp(-a3*x)現(xiàn)有x=[01.0011.999345.02166.99589.002];y=[1513.86912.51511.51410.6479.8959.2448.6798.1897.764];對其用上述非其次指數(shù)函數(shù)擬合，使用非線性回歸函數(shù)nlinfit.程序如下：%%%%%%% x=[01.0011.999345.02166.99589.002];y=[1513.86912.51511.51410.6479.8959.2448.6798.1897.764];myfun=inIine('a(1)+a(2)*exp(-a⑶*x)\"a'f'x1);a=nlinfit(x,y,myfun,[1510,1])I=min(x):0.1:max(x);V=a(1)+a(2)*exp(-a(3)*l);plot(x,y,'o',I,V)legendC'Y1,W1)注意：對于a=nlinfit(x,y,myfun,aO)中關(guān)于aO初始值的選取還需要斟酌！??！選取不當(dāng)可能造成擬合程度不好……結(jié)果如下1.3多個指數(shù)項函數(shù)的擬合擬合函數(shù)模型：y=a(1)*exp(a(2)*x)+a(3)*exp(a(4)*x)程序如下：%%%%%%% X=[0.4906670.9553331.5441.9406672.483.0266673.9666674.4533335.0733336.0333337.04]Y=[253.3333381450503.6667532520489481.3333459438.3333422]myfun=iniine('A⑴*exp(A(2)*x)+A⑶*exp(A(4)*x)"F'A","x')A=nlinfit(X,Y,myfun,[700-0.01-700-1])I=min(X):0.1:max(X);V=A(1)*exp(A(2)*I)+A⑶*exp(A(4)*l);pIOt(X,Y,'o',l,V)legendC'Y1,W1)%%%%%%% 程序結(jié)果如下所示：1.4非其次項的多個指數(shù)項函數(shù)的擬合擬合模型：y=a(1)+a(2)*exp(a(4)*x)+a(3)*exp(-a(4)*x)%%%%%%% x=[1012.51517.52022.52527.53032.53537.54042.54547.550];y=[62.177.392.5104112.9121.9125129.4134138.2142.3143.2144.6147.2147.8149.1150.9];myfunc=iniine(fbeta(1)+beta(2)*exp(beta(3)*x)+beta(4)*exp(-beta⑸*x)",'beta','x');.beta=nIinfit(x,y,myfunc,[0.50.50.50.5,0.5]);a=beta(1),k1=beta(2),k2=beta(4),m=beta(4),n=beta⑸xx=min(x):max(x);yy=a+k1*exp(m*xx)+k2*exp(-n*xx);plot(x,y,"o1,xx,yy,'r')%%%%%%% 結(jié)果如下圖所示：由于蠕變效應(yīng)，地震發(fā)生后，地表地形會發(fā)生蠕變。其蠕