How to fit curve to see the scaling

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!

[Rik]

Are you certain that alpha is an integer? Because then you could just try 0:2 and select the one with the best fit.

If alpha doesn't need to be an integer, there is a wide variety of functions you can use. Which function would be the best choice also depends on whether or not you have access to the curve fitting toolbox.

[Auryn_]

Hi Rik,

actually what I try to do is to find the value of \alpha. It should be certainly a value between 0 and 2.

If I use 1.5 for example the error mentioned above will appear.

I could install any additional tool box if needed.

[Rik]

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_]

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?

Answer 1

[Rik]

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')

[Auryn_]

Awesome, thanks!

[Auryn_]

Hi again!

Could you please help me how to plot the errorbar on the fitted alpha?

Thanks!

[Rik]

You mean like this? Note that for this example data the error bars are quite small.

%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;
CI95=confint(fitobject);
%calculate fit and error bars
y_fit=fitfun(fitted_alpha,x);
y_pos=y_fit-fitfun(CI95(1),x);
y_neg=y_fit-fitfun(CI95(2),x);
%plot in a clean figure
figure(1),clf(1)
errorbar(x,y_fit,y_neg,y_pos,'color','r')
hold on
plot(x,y,'*b')
hold off

[Auryn_]

Thanks, but actually that is not what I meant.

Instead of the error for each of the fitting points, I would like the total error for my fitting parameter alpha.

So, in the case that I have a lot of different curves and for each of them one alpha, if I want to plot all the alphas versus one parameter, how can I show the error bar for the alpha of each curve.

In your example above, I am talking about the total error for the whole fitting.

I hope this is a bit more clear now.

Thanks!

[Rik]

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.

[A_V_G]

Thanks!