MATLAB实例:非线性曲线拟合
MATLAB实例:非线性曲线拟合
作者:凯鲁嘎吉 - 博客园 http://www.cnblogs.com/kailugaji/
用最小二乘法拟合非线性曲线,给出两种方法:(1)指定非线性函数,(2)用傅里叶函数拟合曲线
1. MATLAB程序
clear clc xdata=[0.1732;0.1775;0.1819;0.1862;0.1905;0.1949;0.1992;0.2035;0.2079;0.2122;0.2165;0.2208;0.2252;0.2295;0.2338;0.2384]; ydata=[-3.41709;-4.90887;-6.09424;-6.95362;-7.63729;-8.12466;-8.37153;-8.55049;-8.61958;-8.65326;-8.60021;-8.52824;-8.43502;-8.32234;-8.20419;-8.04472]; %% 指定非线性函数拟合曲线 X0=[1 1]; [parameter,resnorm]=lsqcurvefit(@fun,X0,xdata,ydata); %指定拟合曲线 A=parameter(1); B=parameter(2); fprintf(‘拟合曲线Lennard-Jones势函数的参数A为:%.8f,B为:%.8f‘, A, B); fit_y=fun(parameter,xdata); figure(1) plot(xdata,ydata,‘r.‘) hold on plot(xdata,fit_y,‘b-‘) xlabel(‘r/nm‘); ylabel(‘Fe-C Ec/eV‘); xlim([0.17 0.24]); legend(‘观测数据点‘,‘拟合曲线‘) % legend(‘boxoff‘) saveas(gcf,sprintf(‘Lennard-Jones.jpg‘),‘bmp‘); % print(gcf,‘-dpng‘,‘Lennard-Jones.png‘); %% 用傅里叶函数拟合曲线 figure(2) [fit_fourier,gof]=fit(xdata,ydata,‘Fourier2‘) plot(fit_fourier,xdata,ydata) xlabel(‘r/nm‘); ylabel(‘Fe-C Ec/eV‘); xlim([0.17 0.24]); saveas(gcf,sprintf(‘demo_Fourier.jpg‘),‘bmp‘); % print(gcf,‘-dpng‘,‘demo_Fourier.png‘);
function f=fun(X,r) f=X(1)./(r.^12)-X(2)./(r.^6);
2. 结果
拟合曲线Lennard-Jones势函数的参数A为:0.00000003,B为:0.00103726 fit_fourier = General model Fourier2: fit_fourier(x) = a0 + a1*cos(x*w) + b1*sin(x*w) + a2*cos(2*x*w) + b2*sin(2*x*w) Coefficients (with 95% confidence bounds): a0 = 79.74 (-155, 314.5) a1 = 112.9 (-262.1, 487.9) b1 = 28.32 (-187.9, 244.6) a2 = 24.5 (-114.9, 163.9) b2 = 13.99 (-75.89, 103.9) w = 15.05 (3.19, 26.9) gof = 包含以下字段的 struct: sse: 0.0024 rsquare: 0.9999 dfe: 10 adjrsquare: 0.9999 rmse: 0.0154
Fig 1. Lennard-Jones势函数拟合曲线
Fig 2. 傅里叶函数拟合曲线