Examples of MATLAB: linear curve fit

Examples of MATLAB: linear curve fit

Author: Kailugaji - blog Park  http://www.cnblogs.com/kailugaji/

By least squares fitting the nonlinear curve, two methods are given: (1) specified nonlinear function, (2) fitting curve of the Fourier function

1. MATLAB program

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 ]?
%% specified nonlinear function fitting curve
X0=[1 1];
[Parameter, resnorm] = lsqcurvefit (@ fun, X0, xdata, ydata);% specifying fit curve
A=parameter(1);
B=parameter(2);
fprintf ( 'curve fitting parameters A Lennard-Jones potential function is:% 8f, B is:..% 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 ([00:17 0:24]);
Legend ( 'observations point', 'Fit Curve')
% legend('boxoff') 
saveas(gcf,sprintf('Lennard-Jones.jpg'),'bmp');
% print(gcf,'-dpng','Lennard-Jones.png');
%% fitting curve of the Fourier function
figure(2)
[fit_fourier,gof]=fit(xdata,ydata,'Fourier2')
plot (fit_fourier, xdata, ydata)
xlabel('r/nm');
ylabel('Fe-C Ec/eV');
xlim ([00:17 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. Results

Curve fitting Lennard-Jones potential as a function of the parameters A: 0.00000003, B is: 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)
       ? 1 = 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 = 

  It contains the following fields of struct:

           beg: 0.0024
       rsquare: 0.9999
           dfe: 10
    adjrsquare: 0.9999
          rmse: 0.0154

Potential Fig 1. Lennard-Jones curve fitting function

Fig 2. Fourier function fitting curve