integrating equations obtained from polyfit

2014 1 14
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更新时间：2014 1 15
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Hello,
I have an equation to integrate:
exp(thata(x)-1)*y_f(x)
But I used polyfit to get the theta and the y_f, so i have two vectors. but I want the equation version of the fit, so that I can put it on the integral equation. how can i use those two vectors to be able to compute that integral?
If someone knows how to do this, I'd appreciate the help!
thank you

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Bjorn Gustavsson
Bjorn Gustavsson 2014-1-15

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Well, either you can hope that your function exp(theta(x)-1)*f(x) has an explicit integral (which might be a stretch) and build yourself a symbolic version of the function and then try the integration-power of the symbolic toolbox. Or you could go with matlabs quadrature functions:
quadgk(@(x) exp(polyval(theta_p,x)-1).*polyval(f,x),0,x_star)
That should work provided your function isn't too obscure.
HTH

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davood
davood 2014-1-15
thank you so much. i checked, it seems that my function does not have an explicit integral. using quadgk is great, but it gives me:
(the value of the integral at x_star)-(the value of the integral at 0)
but i only need the value of the integral at x_star. can i do anything about it?
Bjorn Gustavsson
Bjorn Gustavsson 2014-1-15
I don't know how to calculate a unique value of an integral at one point only, primitive functions typically have a constant-of-integration, for example f(x) = x^2 -> F(x) = x^3/3 + C. Maybe something is missing in your problem description?

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Mischa Kim
Mischa Kim 2014-1-14
编辑：Mischa Kim 2014-1-14

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See http://www.mathworks.de/matlabcentral/answers/34612#answer_43412, e.g.,
trapz(x, exp(theta_x - 1).*y_fx)
where theta_x and y_fx are your two vectors.

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davood
davood 2014-1-15
Hi, thank you so much for the help. I'm still a little confused, though! i want to integrate that equation and then find it's value at x_star, where x_star is a constant. it seems that using trapz computes the integral numerically and does not result in an equation, which then i can find it's value at x_star. do you know how can i do this?
Mischa Kim
Mischa Kim 2014-1-15
OK, but that's really a different question from the one you asked. In general, there is no way to "come up" with a reliable symbolic equation based on numeric data points. And you need a symbolic equation to be able to evaluate it at a certain x_star value.

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