How to fit curve to see the scaling

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Auryn_
Auryn_ 2019-1-9
评论： A_V_G 2019-1-24
Hi,
I would like to see the scaling (\alpha) of my curve f(x,y): x^\alpha
Thus, I need to fit my data to a curve but I cannot use the function polyfit as the value of \alpha could be any value between 0 and 2, and I receive the error message:
Index in position 2 is invalid. Array indices must be positive integers or logical values.
Is there any direct method to do this in Matlab?
Thanks in advance!
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Rik
Rik 2019-1-9
What is the exact code that you are currently using? Because you should be fitting your x-y data to something like this
fitfun=@(x,alpha) x.^alpha;
The error doesn't look like you are doing a curve fit.
Auryn_
Auryn_ 2019-1-9
I just did this:
p=polyfit(x,y,1.5);
f1 = polyval(p,x);
plot(x,f1,'r--')
which is obviously wrong.
How can I plot the result of the fitfun function you mentioned?

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Rik
Rik 2019-1-9
That code doesn't work, because your data is not a polynomial. It doesn't make sense to fit to a polynomial if your data is not. The code below will generate some example data, perform the fit, and plot the result.
In this case you could also make an estimation of alpha by taking the x-base log of y. You'll probably have to do that in a loop.
%generate example data
x=linspace(0,20,30);
noise=(rand(size(x))-0.5)*5;
y=x.^1.7 + noise;
%define function
fitfun=@(alpha,x) x.^alpha;
%perform fit
fitobject = fit(x(:),y(:),fitfun,'StartPoint',1);
fitted_alpha=fitobject.alpha;
%plot in a clean figure
figure(1),clf(1)
plot(x,y,'*b',x,fitfun(fitted_alpha,x),'r')
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Rik
Rik 2019-1-24
The second output of the fit functions returns goodness-of-fit parameters, as you can read in the doc. I expect the sse is closest to what you mean.

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