integrating equations obtained from polyfit
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davood
on 14 Jan 2014
Commented: Bjorn Gustavsson
on 15 Jan 2014
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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Accepted Answer
Bjorn Gustavsson
on 15 Jan 2014
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
2 Comments
Bjorn Gustavsson
on 15 Jan 2014
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?
More Answers (1)
Mischa Kim
on 14 Jan 2014
Edited: Mischa Kim
on 14 Jan 2014
trapz(x, exp(theta_x - 1).*y_fx)
where theta_x and y_fx are your two vectors.
2 Comments
Mischa Kim
on 15 Jan 2014
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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