link: https: //zhuanlan.zhihu.com/p/36103034
Source: know almost
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1） polyfit
Code examples below, fitting a cubic curve, and drawing.
x = 0:1:9;
y = [0 2 4 6 8 20 12 14 16 18]
A=polyfit(x,y,3);
z=polyval(A,x);
plot(x,y,'r*',x,z,'b')
1） lsqcurvefit nlinfit
Use lsqcurvefit (least squares fit) or nlinfit. The following example is a cubic curve fit. These two functions can also be fitted exponential functions, trigonometric functions and so on.
x=[0 1 2 3 4 5 6 7 8 9];
y = [0 1 2 3 4 5 + 10 6 7 8 9];% Here, a noise
w = [1 1 1 1 1 0.1 1 1 1 1]; we know that very low noise of heavy weights%
A0 = [1 1 1 1];
f=@(a,x)a(1)+a(2)*x+a(3)*x.*x+a(4)*x.*x.*x;
f1 = lsqcurvefit(f,a,x,y)
f2 = nlinfit(x,y,f,a0)
y1=f(f1,x)
y2=f(f2,x)
plot(x,y,'r*',x,y1,'b',x,y2,'g')
2）cftool
Note that the above fitting, is not entitled to re-fit. w is not functioning, you will find the fitted curve is greater impact noise. The following will be used to reduce noise cftool fitting:
Command line, type: cftool, Enter, will open the cftool window.
In the window, preferably the X data x, the Y data selected y, this case is automatically fitted to a straight line. Note that the important place came: the Weights selected as w, will find a straight line closer to the normal point!
The following article has reference to all types of explanation fit matlab cftool usage and its menu [at Plum homes _404 7]
3) using the fit note, this is the most important fit! cftool can achieve, achieve all-round here.
x=[0;1;2;3;4;5;6;7;8;9];
y = [0; 1; 2; 3; 4; 5 + 10; 6; 7; 8; 9];% Here, a noise
w = [1; 1; 1; 1; 1; 0.1; 1; 1; 1; 1];% We know that noise is very low weights
A0 = [1 1];
plot(x,y,'o')
fo = fitoptions('Method','NonlinearLeastSquares',...
'StartPoint',a0);
ft = fittype('a+x*b','options',fo);
[curve,gof] = fit(x,y,ft,'Weights',w)
hold on
plot(curve,'m')
legend('Data','curve')
hold off
See also:
Fit type for curve and surface fitting
Create or modify fit options object
4) fit to use SmoothingSpline
x=[0;1;2;3;4;5;6;7;8;9];
y = [0; 1; 2; 3; 4; 5 + 10; 6; 7; 8; 9];% Here, a noise
w = [1; 1; 1; 1; 1; 0.2; 1; 1; 1; 1];% we know the weight of the low noise
A0 = [1 1];
plot(x,y,'o')
fo = fitoptions('method','SmoothingSpline','SmoothingParam',0.07,'Weights',w);
ft = fittype('smoothingspline');
f = fit(x,y,ft,fo)
y1= f(x)
hold on
plot(x,y1,'r')
legend('Data','f')
hold off
Unfortunately, the fitting code can not turn C ++
1) write a file fixSmoothingSpline.m, as follows, it is to make a weighted spline fitting,
function y1 = fixSmoothingSpline(x, y, w)%#codegen
f = fit(x,y,'SmoothingSpline','SmoothingParam',0.07,'Weights',w);
y1= f(x);
2) Input the command line coder, the coder transfer window,
3) However, since the above-mentioned document with the words fit, does not support turn C.