Fitting data to integral function

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Sergio Quesada
Sergio Quesada 2018-6-4
评论： Sergio Quesada 2018-6-4
Hi everybody. I'm trying to fit an essemble of data ("r" as x and "texp" as y) by a function defined by an integral:
FC*integral(@(x)exp(-a./x.*log(x)),1,texp)
, were both "FC" and "a" are the parameters to fit, while "texp" are the upper integration limits, which must be equal to the "y" parameters at each point.
Thank you so much !
  2 个评论
Torsten
Torsten 2018-6-4
So you have data (xi,yi) that should be representable by
(texp(i),FC*integral(@(x)exp(-a./x.*log(x)),1,texp(i)))
?
Walter Roberson
Walter Roberson 2018-6-4
What should the expression equal?? Is it
texp = FC*integral(@(x)exp(-a./x.*log(x)),1,texp)
?
Where is your independent variable?

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回答（2 个）

Sergio Quesada
Sergio Quesada 2018-6-4
Exactly, i hace a collection of data (xi,yi) called (r,texp), and the fitting equation must be
texp(r)=FC*integral(@(x)exp(-a./x.*log(x)),1,texp)
thanks!
  1 个评论
Walter Roberson
Walter Roberson 2018-6-4
Where is your independent variable appearing in the model? Is texp(r) intended to convey "the texp that corresponds to r", or is texp somehow intended to be both a function to be applied to r on the left side, but a particular numeric value on the right hand side where it is acting as the upper bounds of the integral ?
Or is texp(r) intended to be multiplication, as in
texp(K) * r(K) == FC * integral(@(x)exp(-a./x.*log(x), 1, texp(K))
and thus
texp(K) == FC / r(K) * integral(@(x)exp(-a./x.*log(x), 1, texp(K))

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Sergio Quesada
Sergio Quesada 2018-6-4
编辑：Sergio Quesada 2018-6-4
"texp" is my independent variable.
I have a collection of (r,texp) data. I have evaluated
FC*integral(@(x) -a./(x*log(x)),1,texp)
for each texp as upper integration limit with arbitrary values of "a" and "FC". Now i need to find the values of " a" and "FC" that best fits the experimental data
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Walter Roberson
Walter Roberson 2018-6-4
fun = @(FCa, r) arrayfun(@(R) FCa(1) * integral(@(x) exp(-FCa(2)./(x.*log(x))), 1, R), r);
FCa = lsqcurvefit(fun, x0, r, texp);
FC = FCa(1); a = FCa(2);
Sergio Quesada
Sergio Quesada 2018-6-4
success! i am so grateful Walter! This works thanks to people like you!
best regards

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