fitting an equation to the curve

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Megha
Megha 2018-11-15
评论： Rik 2018-11-15
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!
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Rik
Rik 2018-11-15
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
Torsten 2018-11-15
It also works with shadowing :-) But I admit that it's not advisable.

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回答（3 个）

KSSV
KSSV 2018-11-15
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
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Megha
Megha 2018-11-15
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

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madhan ravi
madhan ravi 2018-11-15
编辑：madhan ravi 2018-11-15
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')
  1 个评论
Megha
Megha 2018-11-15
编辑：Megha 2018-11-15
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.

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Image Analyst
Image Analyst 2018-11-15
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?
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Torsten
Torsten 2018-11-15
编辑：Torsten 2018-11-15
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
Rik 2018-11-15
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.

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