fit a curve through selected points with own function

Question

Steve 2020-4-20

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回答： Ameer Hamza 2020-4-20

Hey!

I have a problem.. I don't know why I'm having such a hard time figuring it out.

I have data say

x = [1 2 3 4 5 6 7 8]

y = [3 4 5 6 7 8 9 10]

What I need is to plot it, then choose four points (say x=2, y= 4 and x= 4, y= 6 etc)

and make a fit through only these 4 points. The fit should be of the form x**-n, where n is a real number.

I can then play around with n, to find the best fit, once I can get x,y and this fit with 4 selected points on a same graph.

All help is appreciated, thank you!

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Answer 1

Michael Soskind 2020-4-20

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Hi Steve,

With regards to curve fitting, when you choose the points, then you can fit it to any function using lsqcurvefit, since you know x and y.

Here is an example similar to the one you describe above. I select the values you described, and show the result in a plot:

x = [1 2 3 4 5 6 7 8];
y = [3 4 5 6 7 8 9 10];
range = [2,3,4,7];
xdata = x(range); 
ydata = y(range);
fun = @(c, xdata) c(1)*xdata + c(2);
x0 = [1.2,1.8]
coeffs = lsqcurvefit(fun, x0, xdata, ydata);
figure(); hold on;
plot(xdata, ydata, 'o');
plot(xdata, fun(coeffs, xdata))

I hope that helps, and is similar to what you are looking for,

Michael

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Michael Soskind 2020-4-20

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I forgot to mention, the function definition is important, c is an array of the coefficients, and since I use a linear function, I have a slope term and offset term. In your case, you can scale the polynomial and have the power terms selected by the curve fitting routine.

fun = @(c, xdata) c(1)*xdata.^c(2);

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Answer 2

Ameer Hamza 2020-4-20

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https://ww2.mathworks.cn/matlabcentral/answers/519340-fit-a-curve-through-selected-points-with-own-function#answer_427158

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You can use the curve fitting toolbox to find the fit of the form you described in the question

x = [1 2 3 4 5 6 7 8];
y = [3 4 5 6 7 8 9 10];
ft = fittype('x^-n');
fit_model = fit(x([2 4]).',y([2 4]).',ft);
plot(x, y, '+', x, fit_model(x))

you can check the value of n from 'fit_model'

>> fit_model
fit_model = 
     General model:
     fit_model(x) = x^-n
     Coefficients (with 95% confidence bounds):
       n =      -1.327  (-3.497, 0.8423)