How to find inverse of a self written integral function?
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I have defined a function y=iMyF(x) containing an integral written as y=5*log10[4345*\int_0^x du/sqrt(0.3*(1+u)^2+0.7)] so that I can find y for a given value of x. How can I find x for a given value y for this function? I want to use the inverse function to fit a data set using the curve fitting tool.
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Walter Roberson
2020년 11월 28일
편집: Walter Roberson
2020년 11월 28일
Could you confirm that you want the scaled gamma incomplete and not the unscaled?
It looks plausible to me that the sqrt() could be acting on a negative value, leading to complex, but then converted to real by the abs() ? Does that sound accurate?
Walter Roberson
2020년 11월 28일
I see article https://www.researchgate.net/publication/3388532_Inverse_incomplete_gamma_function_and_its_application . Perhaps some of its ideas could be used as steps in developing the expression you need. It would not be easy though.
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Jeff Miller
2018년 5월 12일
No doubt there are more efficient methods for your particular function, but a quick and dirty general approach is to make a function using fzero. I don't do this often, but I think it would look something like this:
function x = myinverse(y, guess)
fun = @(z) (iMyF(z)-y); % parameterized function
x = fzero(fun,guess) % guess is your initial pretty good guess for x
end
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