fitting an equation to the curve

I have set of data X,Y and i would like to fit an equation of the form

.

I want to find for which n, the curev fits the best.

Any help!

[Rik]

What have you tried so far? And where are x and y in your equation?

[Megha]

I hope i am clear now.

I just plotted plot(X,Y), now i need to fit this

[Torsten]

And n is an integer greater than 0 ?

[Megha]

yes

[Torsten]

X=...;
Y=...;
nmax=10;
for i=1:nmax
  Ysim=(sin(X)).^i;
  error(i) = sum((Y-Ysim).^2);
end
[~,iopt]=min(error)

[Megha]

it is not working.

[Torsten]

Could you be a bit more precise ?

Did you fill the dots with your data ? What's the error message ?

[Rik]

You really shouldn't shadow the error function with a variable. Once you rename it, this code should work. I tried implementing fminsearch, but it is difficult to find a good way to select only discrete results.

[Torsten]

It also works with shadowing :-) But I admit that it's not advisable.

Answer 1

[KSSV]

Read about polyfit

N = 100 ; n = 2 ;
x = linspace(0,2*pi,N) ;
y = sin(x).^n ;
% 
p = polyfit(x,y,7);   % you can change 7 here...
x1 = linspace(0,2*pi);
y1 = polyval(p,x1);
figure
plot(x,y,'o')
hold on
plot(x1,y1)
hold off

[Megha]

@KSSV, thank you very much for your kind response.

It really worked for my case!

[KSSV]

Glad to help you. Read about polyfit, know the subject behind it..don't blindly follow the functions..:)

[Megha]

I am sorry, It didnt work. there is some error i guess

[Megha]

It is not the polyfit that i want.

I want the equation of the form Y = after i should fit the curve.

In the above given example as you told we can vary 7, but hwat is 7 here, it is the order of

polynomial equation. not the value of 'n'.

Here, you have already define 'n', but in our case we dont know n

This is like trial and error, where-in, i should check each value of 'n' and find the best fit

[KSSV]

Run a loop with n.

Answer 2

[madhan ravi]

use interp1() with appropriate method:

x = linspace(-2*pi,2*pi,100) ;
xx=linspace(x(1),x(end),1000);
y = sin(x).^7 ;
yy=interp1(x,y,x,'spline')
figure
plot(x,y,'o',x,yy,'r')

[Megha]

I would like to mention i do not want to polyfit the equation.

I have a dataset, Y and angles in X. There is a nearly type of distribution.

So i want to fit the dataset with eqn for different "n" such that i can find best fit.

Answer 3

[Image Analyst]

My favorite fitting function is fitnlm() in the Statistics and Machine Learning toolbox. It could easily find this n. Just attach your data in a .mat file and I can do it for you. You have a non-linear equation in variable n. You could turn it into a linear equation in n by taking the log of the data and then using polyfit, but do you know how that affects the accuracy? Why not use fitnlm() to fit a non-linear model to n right from the start?

[Torsten]

I think it's not advisable to use a fitting tool since sin(x)^n is complex-valued for sin(x)<0 and n not being an integer.

[Rik]

You could just include a lower bound for n. It should be a non-zero integer anyway.

[Torsten]

sin(x)^a is complex-valued if sin(x)<0 and "a" not being an integer. How should this be healed by including a lower bound for "a" ?

[Rik]

Ah, yes, you are right. But as I already mentioned, it doesn't matter. The exponent should be an integer, so this will be a real value for any valid n.