matlab 画非线性曲线,MATLAB实例：非线性曲线拟合

MATLAB实例：非线性曲线拟合

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