Estimate best parameters using lscurvefit

Question

Oscar Nordin 2020-5-26

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https://ww2.mathworks.cn/matlabcentral/answers/534548-estimate-best-parameters-using-lscurvefit

编辑： John D'Errico 2020-5-27

Given two datasets x and y. I have a very complicated function f depending on x, y and 3 parameters a=(a1,a2,a3) and want to find the parameters a that minimizes f.

For example lets say i have:

x=[1,2,3,4,5]

y=[1,3,5,7,9]

=

+

where

is a very complicated function of both a and x and

is a complicated function of only a.

With fminsearch, the min value of f could be found by just creating a function of everything

fun = @(X)func(X);

where func is

and then use

x0=fminsearch(fun,b)

where b = [b1, b2, b3] is an initial guess

But how can i do it with lscurvefit where i need to state x-data and y-data in the arguments?

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Answer 1

John D'Errico 2020-5-27

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https://ww2.mathworks.cn/matlabcentral/answers/534548-estimate-best-parameters-using-lscurvefit#answer_439668

编辑：John D'Errico 2020-5-27

You are getting lost and confused by the names x and y. They are irrelevant. You have 3 parameters. You have 5 data points, numbered here from 1 to 5. lsqcurvefit does not really care about x and y as such.

Your target here is apparently zero for each such data point.

Just create an objective that evaluates the 5 results, and then returns then to lsqcurvefit, AS A FUNCTION of the parameters.

As easily, you could just use lsqnonlin, since your target is zero anyway for all 5 "data points". Just return the vector f_a.