Using polyfit to fit power function including the initial point x=0
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I want to find the equation for data points that are given below
x= [ 0 0.0005 0.001 0.005 0.01 0.05 0.1];
y=[0.43 0.47 0.51 0.77 1 1.9 2.44];
Because the first x component is zero hence I could not include the first data set if I fit it as power function.
Is there a way to fit it as y=y(0) +a*x^m?
Thank you.
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Respuestas (3)
Star Strider
el 9 de Oct. de 2014
You can do a power fit with fminsearch:
x= [ 0 0.0005 0.001 0.005 0.01 0.05 0.1];
y=[0.43 0.47 0.51 0.77 1 1.9 2.44];
xc = linspace(min(x),max(x));
f = @(b,x) b(1).*x.^b(2);
SSE = @(b,f,x,y) sum((y-f(b,x)).^2);
B = fminsearch(@(b) SSE(b,f,x,y), [1;1]);
figure(1)
plot(x, y, 'pr')
hold on
plot(xc, f(B,xc), '-g')
hold off
grid
legend('Data', 'Power Function Fit', 'Location', 'NW')
text(0.05, 1.2, sprintf('\\itf\\rm(\\itx\\rm) = %.1f \\itx\\rm^{%.2f}',B))
producing:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/176037/image.png)
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the cyclist
el 9 de Oct. de 2014
I assume that you mean you want to fit
y == y0 + a * x^m
and you want to estimate values for y0, a, and m.
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Chad Greene
el 9 de Oct. de 2014
x=[0 0.0005 0.001 0.005 0.01 0.05 0.1];
y=[0.43 0.47 0.51 0.77 1 1.9 2.44];
plot(x,y,'ko')
hold on
linearFit = polyfit(x,y,1);
xfit = linspace(0,.1,100);
yfitLinear = linearFit(1)*xfit + linearFit(2);
plot(xfit,yfitLinear,'b')
secondOrderFit = polyfit(x,y,2);
yfitSecondOrder = secondOrderFit(1)*xfit.^2 + secondOrderFit(2)*xfit + secondOrderFit(3);
plot(xfit,yfitSecondOrder,'r')
legend('original data','linear fit','second order fit','location','southeast')
legend boxoff
box off
You could do whatever power of fit you'd like.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/176036/image.png)
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